Mastering Physics Solutions Chapter 24 Alternating Current Circuits
Chapter 24 Alternating Current Circuits Q.1CQ
How can the rms voltage of an ac circuit be nonzero when its average value is zero? Explain.
Solution:
For a complete cycle the voltage oscillates between positive and negative symmetrically. Therefore the sum of symmetric positive and negative values will become zero and therefore the average value of ac – voltage is zero for a complete cycle.
But when we calculate the rms value of ac – voltage we first calculate the square of the voltage Therefore whether the voltage is positive or negative its square is a positive Therefore the rms voltage of ac is always non zero.
Chapter 24 Alternating Current Circuits Q.1P
An ac generator produces a peak voltage of 55 V. What is the rms voltage of this generator?
Solution:
Chapter 24 Alternating Current Circuits Q.2CQ
Why is the current in an ac circuit not always in phase with its voltage?
Solution:
If we take a pure resistive circuit (circuit with out inductors and capacitors). Then the circuit will respond to the current it self. Therefore in a pure resistive circuit current and voltage will be in
same phase.
Where as if we consider the capacitors they do not respond to the current. They respond to the charge The charge will not build up on the capacitor instantaneously. It will take some time to
build up. Therefore for a capacitor when alternative current is applied, the voltage across it lags behind the current.
Also if we consider the inductors. They respond to the rate of change of current. When the current reaches from its largest value to least value the rate of change is more. Therefore the
voltage across the inductor leads the current Therefore if a circuit is having all these elements definitely the circuit cannot be always in phase with its voltage.
Chapter 24 Alternating Current Circuits Q.2P
European Electricity In many European homes the rms voltage available from a wall socket is 240 V. What is the maximum voltage in this case?
Solution:
Chapter 24 Alternating Current Circuits Q.3CQ
Does an LC circuit consume any power? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.3P
An rms voltage of 120 V produces a maximum current of 2.1 A in a certain resistor. Find the resistance of this resistor.
Solution:
Chapter 24 Alternating Current Circuits Q.4CQ
An LC circuit is driven at a frequency higher than its resonance frequency. What can be said about the phase angle, ϕ, for this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.4P
The rms current in an ac circuit with a resistance of 150 Ω is 0.85 A. What are (a) the average and (b) the maximum power consumed by this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.5CQ
An LC circuit is driven at a frequency lower than its resonance frequency. What can be said about the phase angle, ϕ, for this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.5P
A 3.33-kΩ resistor is connected to a generator with a maximum voltage of 141 V. Find (a) the average and (b) the maximum power delivered to this circuit.
Solution:
Chapter 24 Alternating Current Circuits Q.6CQ
In Conceptual Checkpoint 24-3 we considered an ac circuit consisting of a lightbulb in series with an inductor. The effect of the inductor was to cause the bulb to shine less brightly.
Would the same be true in a direct-current (dc) circuit? Explain.
Solution:
No, the same is not true in a direct current.
In the ac circuit we used the inductor to increase the resistance of the circuit. So, that the bulb shines less brightly. But for dc, frequency is zero. Therefore the inductive reactance of the inductor for dc is zero. So the impedance of the circuit will not decrease. Therefore the bulb will shine with same brightness.
Chapter 24 Alternating Current Circuits Q.6P
A“75-watt” lightbulb uses an average power of 75 W when connected to an rms voltage of 120 V. (a) What is the resistance of the lightbulb? (b) What is the maximum current in the bulb? (c) What is the maximum power used by the bulb at any given instant of time?
Solution:
Chapter 24 Alternating Current Circuits Q.7CQ
How do the resistance, capacitive reactance, and inductive reactance change when the frequency in a circuit is increased?
Solution:
Chapter 24 Alternating Current Circuits Q.7P
Square-Wave Voltage I The relationship is valid only for voltages that vary sinusoidally. Find the relationship between Vrms and Vmax for the “square-wave” voltage shown in Figure.
Solution:
Chapter 24 Alternating Current Circuits Q.8CQ
In the analogy between an RLC circuit and a mass on a spring, what is the analog of the current in the circuit? Explain.
Solution:
The current in an RLC circuit is the analog of velocity of the particle in mass spring system.
We have in an RLC circuit charge is analogous to position in spring mass system.
∴ The current = Rate of change of charge is analogous to velocity = Rate of change of position.
Chapter 24 Alternating Current Circuits Q.8P
The reactance of a capacitor is 65 Ω at a frequency of 57Hz. What is its capacitance?
Solution:
Chapter 24 Alternating Current Circuits Q.9CQ
In the analogy between an RLC circuit and a mass on a spring, the mass is analogous to the inductance, and the spring constant is analogous to the inverse of the capacitance. Explain.
Solution:
As from the concept of inertia in mechanics the mass of a body resists changes in its motion.
Also from the concept of electromagnetic induction and inductor resists the change in the current flowing through it. As these two quantities mass and inductance are having similar function.
Therefore mass is analogous to inductive of the inductor.
Also we know that a spring having large spring constant requires more force to stretch it. Therefore for a spring having large spring constant gets little stretch for a given force. i.e., a more is the spring constant less is the displacement of the spring for a given force. At the same time the capacitor with small capacitance will store a small charge for a given voltage.
∴ More is the spring constant less is the displacement for a given force. Less is the capacitance less is the charge stored for a given voltage. But we know that charge and displacement are analogous to each other therefore the spring constant and inverse of capacitance are analogous to each other.
Chapter 24 Alternating Current Circuits Q.9P
The capacitive reactance of a capacitor at 60.0 Hz is 105 Ω. At what frequency is its capacitive reactance 72.5 Ω?
Solution:
Chapter 24 Alternating Current Circuits Q.10CQ
Two RLC circuits have different values of L and C. Is it possible for these two circuits to have the same resonance frequency? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.10P
A 105-μ Fcapacitor is connected to an ac generator with an rms voltage of 20.0 V and a frequency of 100.0 Hz. What is the rms current in this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.11CQ
Can an RLC circuit have the same impedance at two different frequencies? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.11P
The rms voltage across a 0.010-μ F capacitor is 1.8 V at a frequency of 52 Hz. What are (a) the rms and (b) the maximum current through the capacitor?
Solution:
Chapter 24 Alternating Current Circuits Q.12P
An ac generator with a frequency of 30.0 Hz and an rms voltage of 12.0 V is connected to a 45.5-μ F capacitor, (a) What is the maximum current in this circuit? (b) What is the current in the circuit when the voltage across the capacitor is 5.25 V and increasing? (c) What is the current in the circuit when the voltage across the capacitor is 5.25 V and decreasing?
Solution:
Chapter 24 Alternating Current Circuits Q.13P
The maximum current in a 22-μ F capacitor connected to an ac generator with a frequency of 120 Hz is 0.15 A. (a) What is the maximum voltage of the generator? (b) What is the voltage across the capacitor when the current in the circuit is 0.10 A and increasing? (c) What is the voltage across the capacitor when the current in the circuit is 0.10 A and decreasing?
Solution:
Chapter 24 Alternating Current Circuits Q.14P
An rms voltage of 20.5 V with a frequency of 1.00 kHz is applied to a 0.395-μ F capacitor. (a) What is the rms current in this circuit? (b) By what factor does the current change if the frequency of the voltage is doubled? (c) Calculate the current for a frequency of 2.00 kHz.
Solution:
Chapter 24 Alternating Current Circuits Q.15P
A circuit consists of a 1.00-kHz generator and a capacitor. When the rms voltage of the generator is 0.500 V, the rms current in the circuit is 0.430 mA. (a) What is the reactance of the capacitor at 1.00 kHz? (b) What is the capacitance of the capacitor? (c) If the rms voltage is maintained at 0.500 V, what is the rms current at 2.00 kHz? At 10.0 kHz?
Solution:
Chapter 24 Alternating Current Circuits Q.16P
A capacitor has an rms current of 21 mA at a frequency of 60.0 Hz when the rms voltage across it is 14 V. (a) What is the capacitance of this capacitor? (b) If the frequency is increased, will the current in the capacitor increase, decrease, or stay the same? Explain. (c) Find the rms cm-rent in this capacitor at a frequency of 410 Hz.
Solution:
Chapter 24 Alternating Current Circuits Q.17P
A 0.22-μ F capacitor is connected to an ac generator with an rms voltage of 12 V. For what range of frequencies will the rms current in the circuit be less than 1.0 mA?
Solution:
Chapter 24 Alternating Current Circuits Q.18P
At what frequency will a generator with an rms voltage of 504 V produce an rms current of 7.50 mA in a 0.0150-μF capacitor?
Solution:
Chapter 24 Alternating Current Circuits Q.19P
Find the impedance of a60.0-Hz circuit with a 45.5-Ω resistor connected in series with a 95.0-μ F capacitor.
Solution:
Chapter 24 Alternating Current Circuits Q.20P
An ac generator with a frequency of 105 Hz and an rms voltage of 22.5 V is connected in series with a 10.0-kΩ resistor and a 0.250-μ F capacitor. What is the rms current in this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.21P
The rms current in an RC circuit is 0.72 A. The capacitor in this circuit has a capacitance of 13 μ Fand the ac generator has a frequency of 150 Hz and an rms voltage of 95 V. What is the resistance in this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.22P
A 65.0-Hz generator with an rms voltage of 135 V is connected in series to a3.35-kΩresistor and a 1.50-μ F capacitor. Find (a) the rms current in the circuit and (b) the phase angle, ϕ, between the currentand the voltage.
Solution:
Chapter 24 Alternating Current Circuits Q.23P
(a) At what frequency must the circuit in Problem be operated for the current to lead the voltage by 23.0°? (b) Using the frequency found in part (a), find the average power consumed by this circuit.
A 65.0-Hz generator with an rms voltage of 135 V is connected in series to a3.35-kΩresistor and a 1.50-μ F capacitor. Find (a) the rms current in the circuit and (b) the phase angle, , between the currentand the voltage.
Solution:
Chapter 24 Alternating Current Circuits Q.24P
(a) Sketch the phasor diagramfor an ac circuit with a 105-Ω resistor in series with a 32.2-μ F capacitor. The frequency of the generator is 60.0 Hz. (b) If the rms voltage of the generator is 120 V, what is the average power consumed by the circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.25P
Find the power factor for an RC circuit connected to a 70.0-Hz generator with an rms voltage of 155 V. The values of R and C in this circuit are 105 Ω and 82.4 μ F, respectively.
Solution:
Chapter 24 Alternating Current Circuits Q.26P
(a) Determine the power factor for an RC circuit with R = 4.0 kΩ and C = 0.35 μ Fthatis connected to an ac generator with an rms voltage of 24 V and a frequency of 150 Hz. (b) Will the power factor for this circuit increase, decrease, or stay the same if the frequency of the generator is increased? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.27P
Solution:
Chapter 24 Alternating Current Circuits Q.28P
CE Predict/Explain When a long copper wire of finite resistance is connected to an ac generator, as shown in Figure,a certain amount of current flows through the wire. The wire is now wound into a coil of many loops and reconnected to the generator, as indicated in Figure. (a) Is the current supplied to the coil greater than, less than, or the same as the current supplied to the uncoiled wire? (b) Choose the best explanation from among the following:
I. More currentflows in the circuit because the coiled wire is an inductor, and inductors tend to keep the current flowing in an ac circuit.
II. The current supplied to the circuit is the same because the wire is the same. Simply wrapping the wire in a coil changes nothing.
III. Less current is supplied to the circuit because the coiled wire acts as an inductor, which increases the impedance of the circuit.
Solution:
a)
In the circuit (a) the resistance of the wire is R.
In circuit (b) the resistance of the inductor is called as inductive reactance and it is due to the wounding of copper wire.
The inductor impedance is more than the resistance of the wire. So the current supplied to the coil is less than the current supplied to the single copper wire.
b)
As the circuit (b) consists of inductor the impedance of the circuit is increased. So less current is supplied to the circuit.
Hence best explanation is (III)
Chapter 24 Alternating Current Circuits Q.29P
An inductor has a reactance of 56.5 Ω at 75.0 Hz. What is its reactance at 60.0 Hz?
Solution:
Chapter 24 Alternating Current Circuits Q.30P
What is the rms current in a 77.5-mH inductor when it is connected to a 60.0-Hz generator with an rms voltage of 115 V?
Solution:
Chapter 24 Alternating Current Circuits Q.31P
What rms voltage is required to produce an rms current of 2.1 A in a 66-mH inductor at a frequency of 25 Hz?
Solution:
Chapter 24 Alternating Current Circuits Q.32P
A 525-Ω resistor and a 295-mH inductor are connected in series with an ac generator with an rms voltage of 20.0 V and a frequency of 60.0 Hz. What is the rms current in this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.33P
Solution:
Chapter 24 Alternating Current Circuits Q.34P
An ac generator with a frequency of 1.34 kHz and an rms voltage of 24.2 V is connected in series with a 2.00-kΩ resistor and a 315-mH inductor. (a) What is the power factor for this circuit? (b) What is the average power consumed by this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.35P
An rms voltage of 22.2 V with a frequency of 1.00 kHz is applied to a0.290-mH inductor. (a) What is the rms current in this circuit? (b) By what factor does the current change if the frequency of the voltage is doubled? (c) Calculate the current for a frequency of 2.00 kHz.
Solution:
Chapter 24 Alternating Current Circuits Q.36P
A 0.22-μ H inductor is connected to an ac generator with an rms voltage of 12 V. For what range of frequencies will the rms current in the circuit be less than 1.0 mA?
Solution:
Chapter 24 Alternating Current Circuits Q.37P
The phase angle in a certain RL circuit is 76° at a frequency of 60.0 Hz. If R = 2.7 Ω for this circuit, what is the value of the inductance, L?
Solution:
Chapter 24 Alternating Current Circuits Q.38P
Solution:
Chapter 24 Alternating Current Circuits Q.39P
(a) Sketch the phasor diagram for an ac circuit with a 105-Ω resistor in scries with a 22.5-mH inductor. Thefrequency of the generator is 60.0 Hz. (b) If the rms voltage of the generator is 120 V, what is the average power consumed by the circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.40P
In Problem, does the phase angle increase, decrease, or stay the same when the frequency is increased? Verify your answer by calculating the phase angle at 70.0 Hz.
(a) Sketch the phasor diagram for an ac circuit with a 105-Ω resistor in scries with a 22.5-mH inductor. Thefrequency of the generator is 60.0 Hz. (b) If the rms voltage of the generator is 120 V, what is the average power consumed by the circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.41P
A large air conditioner has a resistance of 7.0 Ω and an inductive reactance of 15 Ω. If the air conditioner is powered by a 60.0-Hz generator with an rms voltage of 240 V, find (a) the impedance of the air conditioner, (b) its rms current, and (c) the average power consumed by the air conditioner.
Solution:
Chapter 24 Alternating Current Circuits Q.42P
Square-Wave Voltage III The “square-wave” voltage shown in Figure is applied to an RL circuit. Sketch the shape of the instantaneous voltage across the inductor, assuming the time constant of the circuit is much less than the period of the applied voltage.
Solution:
Chapter 24 Alternating Current Circuits Q.43P
CE An inductor and a capacitor are to be connected to a generator. Will the generator supply more current at high frequency if the inductor and capacitor arc connected in series or in parallel? Explain.
Solution:
When the frequency of the ac generator is high, then the reactance of the inductor is high and the reactance of the capacitor is low.
For very high frequencies the inductor behaves as an open circuit as its reactance is very high and the capacitor behaves as a very low reactance path.
But when a high resistance is connected in series, the resultant resistance of the circuit will becomes high and there by current in the circuit is low.
And when these two are connected in parallel then the current in the circuit will take the low reactance path and therefore the current in the circuit is very high.
Therefore at high frequency the inductor and capacitor should be connected in parallel to get more current from the generator supply.
Chapter 24 Alternating Current Circuits Q.44P
An inductor and a capacitor arc to be connected to a generator. Will the generator supply more current at low frequency if the inductor and capacitor are connected in series or in parallel? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.45P
Predict/Explain (a) When the ac generator in Figure operates at high frequency, is the rms current in the circuit greater than, less than, or the same as when the generator operates at low frequency? (b) Choose the best explanation from among the following:
I. The current is the same because at high frequency the inductor is like an open circuit, and at low frequency the capacitor is like an open circuit. In either case the resistance of the circuit is R.
II. Less current flows at high frequency because in that limit the inductor acts like an open circuit, allowing no current to flow.
III. More current flows at high frequency because in that limit the capacitor acts like an ideal wire of zero resistance.
Solution:
Chapter 24 Alternating Current Circuits Q.46P
Predict/Explain (a) When the ac generator in Figure operates at high frequency, is the rms current in the circuit greater than, less than, or the same as when the generator operates at low frequency? (b) Choose the best explanation from among the following:
I. The current at high frequency is greater because the higher the frequency the more chargethat flows through a circuit.
II. Less current flows at high frequency because in that limit the inductoris like an open circuit and current has only one path to flow through.
III. The inductor has zero resistance, and therefore the resistance of the circuit is the same at all frequencies. As a result the current is the same at all frequencies.
Solution:
Chapter 24 Alternating Current Circuits Q.47P
Predict/Explain (a) When the ac generator in Figure operates at high frequency, is the rms current in the circuit greater than, less than, or the same as when the generator operates at low frequency? (b) Choose the best explanation from among the following:
I. The capacitor has no resistance, and therefore the resistance of the circuit is the same at all frequencies. As a result the current is the same at all frequencies.
II. Less current flows at high frequency because in that limit the capacitor is like an open circuit and current has only one path to flow through.
III. More current flows at high frequency because in that limit the capacitor is like a short circuit and current has two parallel paths to flow through.
Solution:
Chapter 24 Alternating Current Circuits Q.48P
Find the rms voltage across the element in an RLC circuit with R = 9.9 kΩ, C = 0.15 μ F, and L = 25 mH. The generator supplies an rms voltage of 115 V at a frequency of 60.0 Hz.
Solution:
Chapter 24 Alternating Current Circuits Q.49P
What is the impedance of a1.50-k Ω resistor, a 105-mH inductor, and a 12.8-μ F capacitor connected in series with a 60.0-Hz ac generator?
Solution:
Chapter 24 Alternating Current Circuits Q.50P
Consider the circuit shown in Figure. The ac generator in tills circuit has an rms voltage of 65 V. Given that R = 15 Ω and L = 0.22 mH, find the rms current in this circuit in the limit of (a) high frequency and (b) low frequency.
Solution:
Chapter 24 Alternating Current Circuits Q.51P
Consider the circuit shown in Figure. The ac generator in this circuit has an rms voltage of 75 V. Given that R = 15 Ω and C = 41 μ F, find the rms current in this circuit in the limit of (a) high frequency and (b) low frequency.
Solution:
Chapter 24 Alternating Current Circuits Q.52P
What is the phase angle in an RLC circuit with R = 9.9 kΩ, C = 1.5 μ F, and L = 250 mH? The generator supplies an rms voltage of 115 V at a frequency of 60.0 Hz.
Solution:
Chapter 24 Alternating Current Circuits Q.53P
IP An RLC circuit has a resistance of 105 Ω, an inductance of 85.0 mH, and a capacitance of 13.2 μ F.(a) What is the power factor for this circuit when it is connected to a 125-Hz ac generator? (b) Will the power factor increase, decrease, or stay the same if the resistance is increased? Explain. (c) Calculate the power factor for a resistance of 525 Ω.
Solution:
Chapter 24 Alternating Current Circuits Q.54P
An ac voltmeter, which displays the rms voltage between the two points touched by its leads, is used to measure voltages in the circuit shown in Figure. In this circuit, the ac generator has an rms voltage of 6.00 V and a frequency of 30.0 kHz. The inductance in the circuit is 0.300 mH,the capacitance is 0.100 μ F, and the resistance is 2.50 Ω. What is the reading on a voltmeter when it is connected to points (a) A and B, (b) B and C, (c) A and C, and (d) A and D?
Solution:
Chapter 24 Alternating Current Circuits Q.55P
IP Consider the ac circuit shown in Figure, where we assume that the values of R, L, and C are the same as in the previous problem, and that the rms voltage of the generator is still 6.00 V. The frequency of the generator, however, is doubled to 60.0 kHz. Calculate the rms voltage across (a) the resistor, R, (b) the inductor, L, and (c) the capacitor, C. (d) Do you expect the sum of the rms voltages in parts (a), (b), and (c) to be greater than, less than, or equal to 6.00 V? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.56P
(a) Sketch the phasor diagram for an ac circuit with a 105-Ω resistor in series with a 22.5-mH inductor and a 32.2-μ F capacitor. The frequency of the generator is 60.0 Hz. (b) If the rms voltage of the generator is 120 V, what is the average power consumed by the circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.57P
A generator connected to an RLC circuit has an rms voltage of 120 V and an rms current of 34 mA. If the resistance inthe circuit is 3.3 kΩ and the capacitive reactance is 6.6 kΩ, what is the inductive reactance of the circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.58P
Manufacturing Plant Power A manufacturing plant uses 2.22 kW of electric power provided by a 60.0-Hz ac generator with an rms voltage of 485 V. The plant uses this power to run a number of high-inductance electric motors. The plant’s total resistance is R = 25.0 Ω and its inductive reactance is XL = 45.0 Ω. (a) What is the total impedance of the plant? (b) What is the plant’s power factor? (c) What is the rms current used by the plant? (d) Whatcapacitance, connected in series with the power line, will increase the plant’s power factor to unity? (e) If the power factor is unity, how much current is needed to provide the 2.22 kW of power needed by the plant? Compare your answer with the current found in part (c). (Because power-line losses arc proportional to the square of the current, a utility company will charge an industrial user with a low power factor a higher rate per kWh than a company with a power factor close to unity.)
Solution:
Chapter 24 Alternating Current Circuits Q.59P
CE A capacitor and an inductor connected in series have a period of oscillation given by T. At the time t = 0 the capacitor has its maximum charge. In terms of T, what is the first time after t = 0 that (a) the current in the circuit has its maximum value and (b) the energy stored in the electric field is a maximum?
Solution:
Chapter 24 Alternating Current Circuits Q.60P
Predict/Explain In an RLC circuit a second capacitor is added in series to the capacitor already present. (a) Does the resonance frequency increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The resonance frequency stays the same because it depends only on the resistance in the circuit.
II. Adding a capacitor in series increases the equivalent capacitance, and this decreases the resonance frequency.
III. Adding a capacitor in series decreases the equivalent capacitance, and this increases the resonance frequency.
Solution:
Chapter 24 Alternating Current Circuits Q.61P
In an RLC circuit a second capacitor is added in parallel to the capacitor already present. Does the resonance frequency increase, decrease, or stay the same? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.62P
An RLC circuit has a resonance frequency of 2.4 kHz. If the capacitance is 47 μ F, what is the inductance?
Solution:
Chapter 24 Alternating Current Circuits Q.63P
At resonance, the rms current in an RLC circuit is 2.8 A. If the rms voltage of the generator is 120 V, what is the resistance, R?
Solution:
Chapter 24 Alternating Current Circuits Q.64P
The resistance in an RLC circuit is doubled. (a) Does the resonance frequency increase, decrease, or stay the same? Explain. (b) Does the maximum current in the circuit increase, decrease, or stay the same? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.65P
The voltage in a sinusoidally driven RLC circuit leads the current. (a) If we want to bring this circuit into resonance by changing the frequency of the generator, should the frequency be increased or decreased? Explain. (b) If we want to bring this circuit into resonance by changing the inductance instead, should the inductance be increased or decreased? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.66P
A 115-Ω resistor, a 67.6-mH inductor, and a 189-μ F capacitor are connected in series to an ac generator. (a) At what frequency will the current in the circuit be a maximum? (b) At what frequency will the impedance of the circuit be a minimum?
Solution:
Chapter 24 Alternating Current Circuits Q.67P
An ac generator of variable frequency is connected to an RLC circuit with R = 12 Ω, L = 0.15 mH, and C = 0.20 mF. At a frequency of 1.0 kHz, the rms current in the circuit is larger than desired. Should the frequency of the generator be increased or decreased to reduce the current? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.68P
(a) Find the frequency at which a 33-μ F capacitor has the same reactance as a 33-mH inductor. (b) What is the resonance frequency of an LC circuit made with this inductorand capacitor?
Solution:
Chapter 24 Alternating Current Circuits Q.69P
Consider an RLC circuit with R = 105 Ω, L = 518 mH, and C = 0.200 μ F. (a) At what frequency is this circuit in resonance? (b) Find the impedance of this circuit if the frequency has the value found in part (a), but the capacitance is increased to 0.220 μ F. (c) What is the power factor for the situation described in part (b)?
Solution:
Chapter 24 Alternating Current Circuits Q.70P
An RLC circuit has a resonance frequency of 155 Hz. (a) If both L and C are doubled, does the resonance frequency increase, decrease, or stay the same? Explain. (b) Find the resonance frequency when L and C are doubled.
Solution:
Chapter 24 Alternating Current Circuits Q.71P
An RLC circuit has a capacitance of 0.29 μ F. (a) What inductance will produce a resonance frequency of 95 MHz? (b) It is desired that the impedance at resonance be one-fifth the impedance at 11 kHz. What value of R should be used to obtain this result?
Solution:
Chapter 24 Alternating Current Circuits Q.72GP
CE BIO Persistence of Vision Although an incandescent lightbulb appears to shine with constant intensity, this is an artifact of the eye’s persistence of vision. In fact, the intensity of a bulb’s light rises and falls with time due to the alternating current used in household circuits. If you could perceive these oscillations, would you see the light attain maximum brightness 60 or 120 times per second? Explain.
Solution:
In alternating current : the current attains positive maximum and negative maximum in one complete cycle. But the bulb will be brightest when the current is at maximum in either direction.
But the alternating currents used in house hold circuits have the frequency.60Hz
Therefore in one second the current reaches 60 times positive maximum and 60 times negative maximum.
The light will attain maximum brightness for 120 times in a second.
Chapter 24 Alternating Current Circuits Q.73GP
An inductor in an LC circuit has a maximum current of 2.4 A and a maximum energy of 36 mJ. When the current in the inductor is 1.2 A, what is the energy stored in the capacitor.
Solution:
Chapter 24 Alternating Current Circuits Q.74GP
An RLC circuit is driven at its resonance frequency. Is its impedance greater than, less than, or equal to R? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.75GP
Predict/Explain Suppose the circuits shown in Figures and are connected to identical batteries, rather than to ac generators. (a) Assuming the value of R is the same in the two circuits, is the current in Figure greater than, less than, or the same as the current in Figure? (b) Choose the best explanation from among the following:
I. The circuits have the same current because the capacitor acts like an open circuit and the inductor acts like a short circuit.
II. The current in Figure is larger because it has more circuit elements, each of which can carry current.
III. The current in Figure is larger because it has fewer circuit elements, meaning less resistance to current flow.
Solution:
Chapter 24 Alternating Current Circuits Q.76GP
Suppose the circuits shown in Figures and are connected to identical batteries, rather than to ac generators. Assuming the value of R is the same in the two circuits, is the current in Figure greater than, less than, or the same as the current in Figure? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.77GP
Predict/Explain Consider a circuit consisting of a lightbulb and a capacitor, as shown in circuit 2 of Conceptual Checkpoint 24-2. (a) If the frequency of the generator is increased, does the intensity of the lightbulb increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. As the frequency increases it becomes harder to force current through the capacitor, and therefore the intensity of the lightbulb decreases.
II. The intensity of the lightbulb increases because as the frequency becomes higher the capacitor acts more like a short circuit, allowing more current to flow.
III. The intensity of the lightbulb is independent of frequency because the circuit contains a capacitor but not an inductor.
Solution:
Chapter 24 Alternating Current Circuits Q.78GP
Consider a circuit consisting of a lightbulb and an inductor, as shown in Conceptual Checkpoint 24-3. If the frequency of the generator is increased, does the intensity of the lightbulb increase, decrease, or stay the same? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.79GP
A 4.40-μ F and an 8.80-μ F capacitor are connected in parallel to a 60.0-Hz generator operating with an rms voltage of 115 V. What is the rms currentsupplied by the generator?
Solution:
Chapter 24 Alternating Current Circuits Q.80GP
A 40.40-μ F and an 8.80-μ F capacitor are connected in series to a 60.0-Hz generator operating with an rms voltage of 115 V. What is the rms current supplied by the generator?
Solution:
Chapter 24 Alternating Current Circuits Q.81GP
A 10.0-μ F capacitor and a 30.0-μ F capacitor are connected in parallel to an ac generator with a frequency of 60.0 Hz. What is the capacitivc reactance of this pair of capacitors?
Solution:
Chapter 24 Alternating Current Circuits Q.82GP
A generator drives an RLC circuit with the voltage V shown in Figure. The correspond ing current I is also shown in the figure. (a) Is the inductive reactance of this circuit greater than, less than, or equal to its capacitive reactance? Explain. (b) Is the frequency of this generator greater than, less than, or equal to the resonance frequency of the circuit? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.83GP
Consider the RLC circuit shown in Example, and the corresponding phasor diagram given inthe Insight. (a) On the basis of the phasor diagram, can you conclude that the resonance frequency of this circuit is greater than, less than, or equal to 60.0 Hz? Explain. (b) Calculate the resonance frequency for
this circuit. (c) The impedance of this circuit at 60.0 Hz is 226 Ω. What is the impedance at resonance?
Solution:
Chapter 24 Alternating Current Circuits Q.84GP
When a certain resistor is connected to an ac generator with a maximum voltage of 15 V, the average power dissipated in the resistor is 22 W. (a) What is the resistance of the resistor? (b) What is the rms current in the circuit? (c) We know that Pav = l2rmsR, and hence it seems that reducing the resistance should reduce the average power. On the other hand, we also know that Pav = V2rms/R,which suggests that reducing R increases Pav. Which conclusion is correct? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.85GP
A 9.5-Hz generator is connected to a capacitor. If the current in the generator has its maximum value at t = 0, what is the earliest possible time that the voltage across the capacitor is a maximum?
Solution:
Chapter 24 Alternating Current Circuits Q.86GP
The voltage across an inductor reaches its maximum value 25 ms before the current supplied by the generator reaches its maximum value. What is the lowest possible frequency at which the generator operates?
Solution:
Chapter 24 Alternating Current Circuits Q.87GP
Find the average power consumed by an RC circuit connected to a 60.0-Hz generator with an rms voltage of 122 V. The values of R and C in this circuit are 3.30 kΩ and 2.75 μ F,respectively.
Solution:
Chapter 24 Alternating Current Circuits Q.88GP
A 1.15-k Ω resistor and a 505-mH inductor are connected in series to a 1250-Hz generator with an rms voltage of 14.2 V. (a) What is the rms current in the circuit? (b) What capacitance must be inserted in series with the resistor and inductorto reduce the rms current to half the value found in part (a)?
Solution:
Chapter 24 Alternating Current Circuits Q.89GP
Phasor The phasor diagram for an RLC circuit is shown in Figure. (a) If the resistance in this circuit is 525 Ω, what is the impedance? (b) If the frequency inthis circuit is increased, will the impedance increase, decrease, or stay the same? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.90GP
Figure shows the phasor diagram for an RLC circuit in whichthe impedance is 337 Ω. (a) What is the resistance, R, in this circuit? (b) Is this circuit driven at a frequency that is greater than, less than, or equal to the resonance frequency of the circuit? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.91GP
An RLC circuit has a resistance R = 25 Ω and an inductance L = 160 mH, and is connected to an ac generator with a frequency of 55 Hz. The phasor diagram for this circuit is shown in Figure. Find (a) the impedance, Z, and (b) the capacitance, C, for this circuit. (c) If the value of C is decreased, will the impedance of the circuit increase, decrease, or stay the same? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.92GP
IP Black-Box Experiment You are given a sealed box with two electrical terminals. The box contains a 5.00-Ω resistor in series with either an inductor or a capacitor. When you attach an ac generator with an rms voltage of 0.750 V to the terminals of the box, you find that the current increases with increasing frequency. (a) Does the box contain an inductor or a capacitor?
Explain. (b) When the frequency of the generator is 25.0 kHz, the rms current is 87.2 mA. What is the capacitance or inductance of the unknown component in the box?
Solution:
Chapter 24 Alternating Current Circuits Q.93GP
A circuit is constructed by connecting a 1.00-kΩ resistor, a 252-μ F capacitor, and a 515-mH inductor in series. (a) What is the highest frequency at which the impedance of this circuit is equal to 2.00 kΩ? (b) To reduce the impedance of this circuit, should the frequency be increased or decreased from itsvalue in part (a)? Explain.
Solution:
Chapter 24 Alternating Current Circuits Q.94GP
An RLC circuit with R = 25.0 Ω, L = 325 mH, and C = 45.2 μ Fis connected to an ac generator with an rms voltage of 24 V. Determine the average power delivered to this circuit when the frequency of the generator is (a) equal to the resonance frequency, (b) twice the resonance frequency, and (c) half the resonance frequency.
Solution:
Chapter 24 Alternating Current Circuits Q.95GP
A Light-Dimmer Circuit The intensity of a lightbulb with aresistance of 120 Ω is controlled by connecting it in series with an inductor whose inductance can be varied from L = 0 to L = Lmax. This “light dimmer”circuit is connected to an ac generator with a frequency of 60.0 Hz and an rms voltage of 110 V. (a) What is the average power dissipated in the lightbulb when L = 0? (b) The inductor is now adjusted so that L = Lmax. In this case, the average power dissipated in the lightbulb is one-fourth the value found in part(a). What is the value of Lmax?
Solution:
Chapter 24 Alternating Current Circuits Q.96GP
An electric motor with a resistance of 15 Ω and an inductance of 53 mH is connected to a 60.0-Hz ac generator. (a) What is the power factor for this circuit? (b) In order to increase the power factor of this circuit to 0.80, a capacitor is connected in series with the motor and inductor. Find the required value of the capacitance.
Solution:
Chapter 24 Alternating Current Circuits Q.97GP
Tuning a Radio A radio tuning circuit contains an RLC circuit with R = 5.0 Ω and L = 2.8 μ H.(a) What capacitance is needed to produce a resonance frequency of 85 MHz?
(b) If the capacitance is increased above the value found in part (a), will the impedance increase, decrease, or stay the same? Explain. (c) Find the impedance of the circuit at resonance. (d) Find the impedance of the circuit when the capacitance is 1% higherthan the value found in part (a).
Solution:
Chapter 24 Alternating Current Circuits Q.98GP
If the maximum voltage in the square wave shown in Figure is Vmax, what are (a) the average voltage, Vav, and (b) the rms voltage, Vrms?
Solution:
Chapter 24 Alternating Current Circuits Q.99GP
An ac generator supplies anrms voltage of 5.00 V to an RC circuit. At a frequency of 20.0 kHz the rms current in the circuit is 45.0 mA; at a frequency of 25.0 kHz the rms current is 50.0 mA. What are the vahtes of R and C in this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.100GP
An ac generator supplies an rms voltage of 5.00 V to an RL circuit. At a frequency of 20.0 kHz the rms current in the circuit is 45.0 mA; at afrequency of 25.0 kHz the rms current is 40.0 mA. What are the values of R and L in this circuit?
Solution:
Chapter 24 Alternating Current Circuits Q.101GP
Solution:
Chapter 24 Alternating Current Circuits Q.102PP
Suppose a theremin uses an oscillator with a fixed frequency of 90.1 MHz and an RLC circuit with R = 1.5 Ω, L = 2.08 μH, and C = 1.50pF. What is the beat frequency of these two oscillators? (Audio frequencies range from about 20 Hz to 20,000 Hz.)
A. 3740 Hz
B. 5100 Hz
C. 4760 Hz
D. 9000 Hz
Solution:
Chapter 24 Alternating Current Circuits Q.103PP
If the thereminist moves one of her fingers and increases the capacitance of the system slightly, does the beat frequency increase, decrease, or stay the same?
Solution:
Chapter 24 Alternating Current Circuits Q.104PP
Find the new beat frequency if the thereminist increases the capacitance by 0.100% over its value inProblem 102. All other quantities stay the same.
A. 761 Hz
B. 41,300 Hz
C. 41,900 Hz
D. 86,300 Hz
Solution:
Chapter 24 Alternating Current Circuits Q.105PP
What is the rms current in the therernm’s RLC circuit (Problem) if it is attached to an ac generator with an rms voltage of 25.0 V and a frequency of 90.0 MHz?
A. 2.14 mA
B. 3.46 mA
C. 8.06 A
D. 16.7 A
Suppose a theremin uses an oscillator with a fixed frequency of 90.1 MHz and an RLC circuit with R = 1.5 Ω, L = 2.08 μH, and C = 1.50pF. What is the beat frequency of these two oscillators? (Audio frequencies range from about 20 Hz to 20,000 Hz.)
A. 3740 Hz
B. 5100 Hz
C. 4760 Hz
D. 9000 Hz
Solution:
Chapter 24 Alternating Current Circuits Q.106IP
IP Referring to Example Suppose we would like to change the phase angle for this circuit to ϕ = −25.0°, and that we would like to accomplish this by changing the resistor to a value other than 175 Ω. The inductor is still 90.0 mH, the capacitor is 15.0 μ F, the rms voltage is 120.0 V, and the ac frequency is 60.0 Hz. (a) Should the resistance be increased or decreased? Explain. (b) Find the resistance that gives the desired phase angle. (c) What is the rms current in the circuit with the resistance found in part (b)?
Solution:
Chapter 24 Alternating Current Circuits Q.107IP
Referring to Example You plan to change the frequency of the generator in this circuit to produce a phase angle of smaller magnitude. The resistor is still 175 Ω, the inductor is 90.0 mH, the capacitor is 15.0 μ F,and the rms voltage is 120.0 V.
(a) Should you increase or decrease the frequency? Explain.
(b) Find the frequency that gives aphase angle of −22.5°.
(c) What is the rms current in the circuit at the frequency found in part (b)?
Solution:
