Chap 31

A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm and released from rest. In the electrical analog the maximum charge on the capacitor is 0.25 C. The maximum current in the LC circuit is: A. 0.38 A B. 0.025 A C. 40 A D. 2.3 A E. 5.3 A

A

A 35-µF capacitor is connected to a source of sinusoidal emf with a frequency of 400 Hz and a maximum emf of 20 V. The maximum current is: A. 0 B. 0.28 A C. 1.8 A D. 230 A E. 1400 A

C

The units of the power factor are: A. ohm B. watt C. radian D. ohm1/2 E. none of these

E

A generator supplies 100 V to the primary coil of a transformer. The primary has 50 turns and the secondary has 500 turns. The secondary voltage is: A. 1000 V B. 500 V C. 250 V D. 100 V E. 10 V

A

A series RC circuit is connected to an emf source having angular frequency ω. The current: A. leads the source emf by tan−1(1/ωCR) B. lags the source emf by tan−1(1/ωCR) C. leads the source emf by tan−1(ωCR) D. lags the source emf by tan−1(ωCR) E. leads the source emf by π/4

A

A series circuit with an inductance of 15 mH, a capacitance of 35 µF, and a resistance of 5.0 Ω contains a sinusoidal source of emf with a frequency of 500 Hz. The frequency with which the charge on the capacitor oscillates is: A. 500 Hz B. 1.4 kHz C. greater than 1.4 kHz D. less than 500 Hz E. between 500 Hz and 1.4 kHz

A

An RLC circuit has an inductance of 25 mH and a capacitance of 5.0 µF. The charge on the capacitor does NOT oscillate but rather decays exponentially to zero. The resistance in the circuit must be: A. greater than or equal to 20, 000Ω B. less than 20, 000Ω but greater than 10, 000Ω C. less than 10, 000Ω but greater than 5, 000Ω D. less than 5, 000Ω but greater than 0 E. 0 ans: A

A

In a purely capacitive circuit the current: A. leads the voltage by one-fourth of a cycle B. leads the voltage by one-half of a cycle C. lags the voltage by one-fourth of a cycle D. lags the voltage by one-half of a cycle E. is in phase with the potential difference across the plates

A

In a sinusoidally driven series RLC circuit the current lags the applied emf. The rate at which energy is dissipated in the resistor can be increased by: A. decreasing the capacitance and making no other changes B. increasing the capacitance and making no other changes C. increasing the inductance and making no other changes D. increasing the driving frequency and making no other changes E. decreasing the amplitude of the driving emf and making no other changes

A

The graphs show the total electromagnetic energy in two RLC circuits as functions of time. Which of the following statements might be true? A. Circuit 1 has a smaller resistance and a larger inductance B. Circuit 1 has a larger resistance and a smaller inductance C. Circuit 1 has the same resistance and a larger inductance D. Circuit 1 has a larger resistance and a larger capacitance E. Circuit 1 has the same resistance and a smaller capacitance

A

The primary of a 3 : 1 step-up transformer is connected to a source and the secondary is connected to a resistor R. The power dissipated by R in this situation is P. If R is connected directly to the source it will dissipate a power of: A. P/9 B. P/3 C. P D. 3P E. 9P

A

The resistance of the primary coil of a well-designed, 1 : 10 step-down transformer is 1 Ω. With the secondary circuit open, the primary is connected to a 12 V ac generator. The primary current is: A. essentially zero B. about 12 A C. about 120 A D. depends on the actual number of turns in the primary coil E. depends on the core material

A

A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum energy of 360 µJ. At a certain instant the energy in the capacitor is 40 µJ. At that instant what is the potential difference across the capacitor? A. zero B. 5 V C. 10 V D. 15 V E. 20 V

B

A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time after t = 0 that the current is a maximum is: A. T B. T /4 C. T /2 D. T E. 2T

B

A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time after t = 0 that the energy stored in the magnetic field of the inductor is a maximum is: A. T B. T /4 C. T /2 D. T E. 2T

B

A resistor, an inductor, and a capacitor are connected in parallel to a sinusoidal source of emf. Which of the following is true? A. The currents in all branches are in phase. B. The potential differences across all branches are in phase. C. The current in the capacitor branch leads the current in the inductor branch by one-fourth of a cycle D. The potential difference across the capacitor branch leads the potential difference across the inductor branch by one-fourth of a cycle. E. The current in the capacitor branch lags the current in the inductor branch by one-fourth of a cycle.

B

A series RL circuit is connected to an emf source of angular frequency ω. The current: A. leads the applied emf by tan−1(ωL/R) B. lags the applied emf by tan−1(ωL/R) C. lags the applied emf by tan−1(ωR/L) D. leads the applied emf by tan−1(ωR/L) E. is zero

B

An RLC circuit has a capacitance of 12 µF, an inductance of 25 mH, and a resistance of 60Ω. The current oscillates with an angular frequency of: A. 1.2 × 103 rad/s B. 1.4 × 103 rad/s C. 1.8 × 103 rad/s D. 2.2 × 103 rad/s E. 2.6 × 103 rad/s

B

An RLC series circuit has L = 100 mH and C = 1 µF. It is connected to a 1000-Hz source and the source emf is found to lead the current by 75◦. The value of R is: A. 12.6 Ω B. 126 Ω C. 175 Ω D. 1750 Ω E. 1810 Ω

B

An RLC series circuit is driven by a sinusoidal emf with angular frequency ωd. If ωd is increased without changing the amplitude of the emf the current amplitude increases. If L is the inductance, C is the capacitance, and R is the resistance, this means that: A. ωdL > 1/ωdC B. ωdL < 1/ωdC C. ωdL = 1/ωdC D. ωdL>R E. ωdL<R

B

An RLC series circuit, connected to a source E, is at resonance. Then: A. the voltage across R is zero B. the voltage across R equals the applied voltage C. the voltage across C is zero D. the voltage across L equals the applied voltage E. the applied voltage and current differ in phase by 90

B

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-Ω resistor, a 400-mH inductor, and a 200-µF capacitor. The rms current in amperes is: A. 0.125 B. 0.135 C. 0.18 D. 0.20 E. 0.40 ans: B

B

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-Ω resistor, a 400-mH inductor, and a 200-µF capacitor. The rms voltage (in volts) across the capacitor is: A. 2.5 B. 3.4 C. 6.7 D. 10.0 E. 10.8

B

An electric motor, under load, has an effective resistance of 30 Ω and an inductive reactance of 40 Ω. When powered by a source with a maximum voltage of 420 V, the maximum current is: A. 6.0 A B. 8.4 A C. 10.5 A D. 12.0 A E. 14.0 A

B

In an ideal 1 : 8 step-down transformer, the primary power is 10 kW and the secondary current is 25 A. The primary voltage is: A. 25, 600 V B. 3200 V C. 400 V D. 50 V E. 6.25 V

B

Radio receivers are usually tuned by adjusting the capacitor of an LC circuit. If C = C1 for a frequency of 600 kHz, then for a frequency of 1200 kHz one must adjust C to: A. C1/2 B. C1/4 C. 2C1 D. 4C1 E. √2C1

B

The average power supplied to the circuit shown passes through a maximum when which one of the following is increased continuously from a very low to a very high value? .......................................................................................... E, f C A. Source emf E B. R C. C D. Source frequency f E. None of these

B

The main reason that alternating current replaced direct current for general use is: A. ac generators do not need slip rings B. ac voltages may be conveniently transformed C. electric clocks do not work on dc D. a given ac current does not heat a power line as much as the same dc current E. ac minimizes magnetic effects

B

n a purely inductive circuit, the current lags the voltage by: A. zero B. one-fourth of a cycle C. one-half of a cycle D. three-fourths of a cycle E. one cycle

B

A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum energy of 360 µJ. At a certain instant the energy in the capacitor is 40 µJ. At that instant what is the emf induced in the inductor? A. zero B. 5 V C. 10 V D. 15 V E. 20 V

C

A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time after t = 0 that the energy stored in the electric field of the capacitor is a maximum is: A. T B. T /4 C. T /2 D. T E. 2T

C

A coil has a resistance of 60 Ω and an impedance of 100 Ω. Its reactance, in ohms, is: A. 40 B. 60 C. 80 D. 117 E. 160

C

A series circuit consists of a 15-Ω resistor, a 25-mH inductor, and a 35-µF capacitor. If the frequency is 100 Hz the power factor is: A. 0 B. 0.20 C. 0.45 D. 0.89 E. 1.0

C

An LC circuit has a capacitance of 30 µF and an inductance of 15 mH. At time t = 0 the charge on the capacitor is 10 µC and the current is 20 mA. The maximum current is: A. 18 mA B. 20 mA C. 25 mA D. 35 mA E. 42 mA

C

An LC circuit has an inductance of 20 mH and a capacitance of 5.0 µF. At time t = 0 the charge on the capacitor is 3.0 µC and the current is 7.0 mA. The total energy is: A. 4.1 × 10−7 J B. 4.9 × 10−7 J C. 9.0 × 10−7 J D. 1.4 × 10−6 J E. 2.8 × 10−6 J

C

An LC series circuit with an inductance L and a capacitance C has an oscillation frequency f. Two inductors, each with inductance L, and two capacitors, each with capacitance C, are all wired in series and the circuit is completed. The oscillation frequency is: A. f /4 B. f /2 C. f D. 2f E. 4f

C

An RL series circuit is connected to an ac generator with a maximum emf of 20 V. If the maximum potential difference across the resistor is 16 V, then the maximum potential difference across the inductor is: A. 2 V B. 4 V C. 12 V D. 25.6 V E. 36 V

C

An RLC circuit has a resistance of 200 Ω and an inductance of 15 mH. Its oscillation frequency is 7000 Hz. At time t = 0 the current is 25 mA and there is no charge on the capacitor. After five complete cycles the current is: A. zero B. 1.8 × 10−6 A C. 2.1 × 10−4 A D. 2.3 × 10−3 A E. 2.5 × 10−2 A

C

An RLC circuit has a sinusoidal source of emf. The average rate at which the source supplies energy is 5 nW. This must also be: A. the average rate at which energy is stored in the capacitor B. the average rate at which energy is stored in the inductor C. the average rate at which energy is dissipated in the resistor D. twice the average rate at which energy is stored in the capacitor E. three times the average rate at which energy is stored in the inductor

C

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-Ω resistor, a 400-mH inductor, and a 200-µF capacitor. The rms voltage (in volts) across the resistor is: A. 2.5 B. 3.4 C. 6.7 D. 10.0 E. 10.8

C

Iron, rather than copper, is used in the core of transformers because iron: A. can withstand a higher temperature B. has a greater resistivity C. has a very high permeability D. makes a good permanent magnet E. insulates the primary from the secondary

C

The angular frequency of a certain RLC series circuit is ω0. A source of sinusoidal emf, with angular frequency 2ω, is inserted into the circuit. After transients die out the angular frequency of the current oscillations is: A. ω0/2 B. ω0 C. 2ω0 D. 1.5ω0 E. 3ω0

C

The angular frequency of a certain RLC series circuit is ω0. A source of sinusoidal emf, with angular frequency ω, is inserted into the circuit and ω is varied while the amplitude of the source is held constant. For which of the following values of ω is the amplitude of the current oscillations the greatest? A. ω0/5 B. ω0/2 C. ω0 D. 2ω0 E. None of them (they all produce the same current amplitude) ans:

C

The ideal meters shown read rms current and voltage. The average power delivered to the load is: unknown load A. definitely equal to V I B. definitely more than V I C. possibly equal to V I even if the load contains an inductor and a capacitor D. definitely less than V I E. zero, as is the average of any sine wave

C

The rms value of an ac current is: A. its peak value B. its average value C. that steady current that produces the same rate of heating in a resistor as the actual current D. that steady current that will charge a battery at the same rate as the actual current E. zero

C

The total energy in an LC circuit is 5.0 × 10−6 J. If L = 25 mH the maximum current is: A. 10 mA B. 14 mA C. 20 mA D. 28 mA E. 40 mA

C

We desire to make an LC circuit that oscillates at 100 Hz using an inductance of 2.5 H. We also need a capacitance of: A. 1 F B. 1 mF C. 1 µF D. 100 µF E. 1 pF

C

An LC circuit has a capacitance of 30 µF and an inductance of 15 mH. At time t = 0 the charge on the capacitor is 10 µC and the current is 20 mA. The maximum charge on the capacitor is: A. 8.9 µC B. 10 µC C. 12 µC D. 17 µC E. 24 µC

D

An ac generator produces 10 V (rms) at 400 rad/s. It is connected to a series RL circuit (R = 17.3 Ω, L = 0.025 H). The rms current is: A. 0.50 A and leads the emf by 30◦ B. 0.71 A and lags the emf by 30◦ C. 1.40 A and lags the emf by 60◦ D. 0.50 A and lags the emf by 30◦ E. 0.58 A and leads the emf by 90◦

D

The impedance of an RLC series circuit is definitely increased if: A. C decreases B. L increases C. L decreases D. R increases E. R decreases

D

The primary of an ideal transformer has 100 turns and the secondary has 600 turns. Then: A. the power in the primary circuit is less than that in the secondary circuit B. the currents in the two circuits are the same C. the voltages in the two circuits are the same D. the primary current is six times the secondary current E. the frequency in the secondary circuit is six times that in the primary circui

D

The rapid exponential decay in just a few cycles of the charge on the plates of capacitor in an RLC circuit might be due to: A. a large inductance B. a large capacitance C. a small capacitance D. a large resistance E. a small resistance

D

The rms value of a sinusoidal voltage is V0/ √2, where V0 is the amplitude. What is the rms value of its fully rectified wave? Recall that Vrect(t) = |V A. V 20 /√2 B. V 20 /2 C. √2V0 D. V0/√2 E. V0/(2√2)

D

The core of a transformer is made in a laminated form to: A. facilitate easy assembly B. reduce i 2R losses in the coils C. increase the magnetic flux D. save weight E. prevent eddy currents

E

The impedance of the circuit shown is: 50 Hz, 240 Vrms A. 21 Ω B. 50 Ω C. 63 Ω D. 65 Ω E. 98 Ω

E

When the amplitude of the oscillator in a series RLC circuit is doubled: A. the impedance is doubled B. the voltage across the capacitor is halved C. the capacitive reactance is halved D. the power factor is doubled E. the current amplitude is doubled

E

n a purely resistive circuit the current: A. leads the voltage by one-fourth of a cycle B. leads the voltage by one-half of a cycle C. lags the voltage by one-fourth of a cycle D. lags the voltage by one-half of a cycle E. is in phase with the voltage

E

3. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time after t = 0 that the voltage across the inductor is a maximum is: A. T B. T /4 C. T /2 D. T E. 2T

C

A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm and released from rest. In the electrical analog the initial charge on the capacitor is: A. 0.15 C B. 6.67 C C. 0.025 C D. 40 C E. 35 C

C

In an RLC series circuit, which is connected to a source of emf Em cos(ωt), the current lags the voltage by 45◦ if: A. R = 1/ωC − ωL B. R = 1/ωL − ωC C. R = ωL − 1/ωC D. R = ωC − 1/ωL E. ωL = 1/ωC

C

In an oscillating LC circuit, the total stored energy is U. The maximum energy stored in the capacitor during one cycle is: A. U/2 B. U/√2 C. U D. U/(2π) E. U/π

C

At time t = 0 the charge on the 50-µF capacitor in an LC circuit is 15 µC and there is no current. If the inductance is 20 mH the maximum current is: A. 15 nA B. 15 µA C. 6.7 mA D. 15 mA E. 15 A

D

9. An LC circuit consists of a 1-µF capacitor and a 4 mH inductor. Its oscillation frequency is approximately: A. 0.025 Hz B. 25 Hz C. 60 Hz D. 2500 Hz E. 15, 800 Hz

D

A sinusoidal voltage V (t) has an rms value of 100 V. Its maximum value is: A. 100 V B. 707 V C. 70.7 V D. 141 V E. 200 V

D

A step-down transformer is used to: A. increase the power B. decrease the power C. increase the voltage D. decrease the voltage E. change ac to dc

D

In the diagram, the function y(t) = ym sin(ωt) is plotted as a solid curve. The other three curves have the form y(t) = ym sin(ωt + φ), where φ is between −π/2 and +π/2. Rank the curves according to the value of φ, from the most negative to the most positive. t y(t) A. 1, 2, 3 B. 2, 3, 1 C. 3, 2, 1 D. 1, 3, 2 E. 2, 1, 3

D

The electrical analog of a spring constant k is: A. L B. 1/L C. C D. 1/C E. R

D

The reactance in ohms of a 35-µF capacitor connected to a 400-Hz generator is: A. 0 B. 0.014 C. 0.088 D. 11 E. 71

D

Which of the following has the greatest effect in decreasing the oscillation frequency of an LC circuit? Using instead: A. L/2 and C/2 B. L/2 and 2C C. 2L and C/2 D. 2L and 2C E. none of these

D

An LC circuit has an inductance of 15 mH and a capacitance of 10 µF. At one instant the charge on the capacitor is 25 µC. At that instant the current is changing at the rate of: A. 0 B. 1.7 × 10−8 A/s C. 5.9 × 10−3 A/s D. 3.8 × 10−2 A/s E. 170 A/s

E

An RLC series circuit is connected to an oscillator with a maximum emf of 100 V. If the voltage amplitudes VR, VL, and VC are all equal to each other, then VR must be: A. 33 V B. 50 V C. 67 V D. 87 V E. 100 V

E

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-Ω resistor, a 400-mH inductor, and a 200-µF capacitor. The rms voltage (in volts) across the inductor is: A. 2.5 B. 3.4 C. 6.7 D. 10.0 E. 10.8

E

In a series RLC circuit the rms value of the generator emf is E and the rms value of the current is i. The current lags the emf by φ. The average power supplied by the generator is given by: A. (iE/2) cos φ B. iE C. i 2/Z D. i2Z E. i2R

E

In a sinusoidally driven series RLC circuit, the inductive reactance is XL = 200 Ω, the capacitive reactance is XC = 100 Ω, and the resistance is R = 50 Ω. The current and applied emf would be in phase if: A. the resistance is increased to 100 Ω, with no other changes B. the resistance is increased to 200 Ω, with no other changes C. the inductance is reduced to zero, with no other changes D. the capacitance is doubled, with no other changes E. the capacitance is halved, with no other changes`

E

In an oscillating LC circuit, the total stored energy is U and the maximum charge on the capacitor is Q. When the charge on the capacitor is Q/2, the energy stored in the inductor is: A. U/2 B. U/4 C. (4/3)U D. 3U/2 E. 3U/4

E

An RLC series circuit has R = 4 Ω, XC = 3 Ω, and XL = 6 Ω. The impedance of this circuit is: A. 5 Ω B. 7 Ω C. 9.8 Ω D. 13 Ω E. 7.8 Ω

A

. A capacitor in an LC oscillator has a maximum potential difference of 15 V and a maximum energy of 360 µJ. At a certain instant the energy in the capacitor is 40 µJ. At that instant what is the potential difference across the capacitor? A. zero B. 5 V C. 10 V D. 15 V E. 20 V

B

. In an RLC series circuit, the source voltage is leading the current at a given frequency f. If f is lowered slightly, then the circuit impedance will: A. increase B. decrease C. remain the same D. need to know the amplitude of the source voltage E. need to know whether the phase angle is larger or smaller than 45◦ ans: B

B

When the frequency of the oscillator in a series RLC circuit is doubled: A. the capacitive reactance is doubled B. the capacitive reactance is halved C. the impedance is doubled D. the current amplitude is doubled E. the current amplitude is halved

B

. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time after t = 0 that the charge on the capacitor is a maximum is: A. T B. T /4 C. T /2 D. T E. 2T

C

. A source with an impedance of 100 Ω is connected to the primary coil of a transformer and a resistance R is connected to the secondary coil. If the transformer has 500 turns in its primary coil and 100 turns in its secondary coil the greatest power will be dissipated in the resistor if R =: A. 0 B. 0.25 Ω C. 4.0 Ω D. 50 Ω E. 100 Ω

C

10. An LC circuit has an oscillation frequency of 105 Hz. If C = 0.1 µF, then L must be about: A. 10 mH B. 1 mH C. 25 µH D. 2.5 µH E. 1 pH

C

The total energy in an LC circuit is 5.0 × 10−6 J. If C = 15 µF the charge on the capacitor is: A. 0.82 µC B. 8.5 µC C. 12 µC D. 17 µC E. 24 µC

C