Question 1

The impedance of the circuit shown is:

Accepted Answer

A)  21 $\Omega$ 
B)  50 $\Omega$ 
C)  63  $\Omega$ 
D)  65  $\Omega$ 
E)  98  $\Omega$ 
A)  21 $\Omega$ 
B)  50 $\Omega$ 
C)  63  $\Omega$ 
D)  65  $\Omega$ 
E)  98  $\Omega$ D

Question 2

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:

Accepted Answer

A)  U/2 
B)  U/4 
C)  (4/3)U 
D)  3U/2 
E)  3U/4 
A)  U/2 
B)  U/4 
C)  (4/3)U 
D)  3U/2 
E)  3U/4 E

Question 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 energy stored in the magnetic field of the inductor is a maximum is:

Accepted Answer

A)  T/4 
B)  T/2 
C)  T 
D)  3T/2 
E)  2T 
A)  T/4 
B)  T/2 
C)  T 
D)  3T/2 
E)  2T A

Question 4

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50-$\Omega$ resistor, a 400-mH inductor, and a 200-$\mu$F capacitor. The rms voltage across the resistor is:

Accepted Answer

A)  2.5 V 
B)  3.4 V 
C)  6.7 V 
D)  10.0 V 
E)  10.8 V 
A)  2.5 V 
B)  3.4 V 
C)  6.7 V 
D)  10.0 V 
E)  10.8 V

Question 5

In the diagram, the function y(t) = ymsin($ \omega $t) is plotted as a solid curve. The other three curves have the form y(t) = ymsin($ \omega $t + $\phi$ ), where $\phi$  is between - $\pi$/2 and + $\pi$/2. Rank the curves according to the value of $\phi$ , from the most negative to the most positive.

Accepted Answer

A)  1, 2, 3 
B)  2, 3, 1 
C)  3, 2, 1 
D)  1, 3, 2 
E)  2, 1, 3 
A)  1, 2, 3 
B)  2, 3, 1 
C)  3, 2, 1 
D)  1, 3, 2 
E)  2, 1, 3

Question 6

The resistance of the primary coil of a well-designed, 1:10 step-down transformer is 1  $\Omega$. With the secondary circuit open, the primary is connected to a 12 V ac generator. The primary current is:

Accepted Answer

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)  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

Question 7

An RLC series circuit is driven by a sinusoidal emf with angular frequency   $ \omega $d. If   $ \omega $d 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:

Accepted Answer

A) $ \omega $dL > 1/ $ \omega $dC B) $ \omega $dL dC C) $ \omega $dL = 1/ $ \omega $dC D) $ \omega $dL > R E) $ \omega $dL < R A) $ \omega $dL > 1/ $ \omega $dC B) $ \omega $dL dC C) $ \omega $dL = 1/ $ \omega $dC D) $ \omega $dL > R E) $ \omega $dL < R

Question 8

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:

Accepted Answer

A)  33 V 
B)  50 V 
C)  67 V 
D)  87 V 
E)  100 V 
A)  33 V 
B)  50 V 
C)  67 V 
D)  87 V 
E)  100 V

Question 9

A sinusoidal voltage V(t) has an rms value of 100 V. Its maximum value is:

Accepted Answer

A)  70.7 V 
B)  100 V 
C)  141 V 
D)  200 V 
E)  707 V 
A)  70.7 V 
B)  100 V 
C)  141 V 
D)  200 V 
E)  707 V

Question 10

A 35-$\mu$F capacitor is connected to an ac source of emf with a frequency of 400 Hz and a maximum emf of 20 V. The maximum current is:

Accepted Answer

A)  0 A 
B)  0.28 A 
C)  1.8 A 
D)  230 A 
E)  1400 A 
A)  0 A 
B)  0.28 A 
C)  1.8 A 
D)  230 A 
E)  1400 A

Question 11

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:

Accepted Answer

A)  0.15 C 
B)  0.25 C 
C)  8.8 C 
D)  15 C 
E)  35 C 
A)  0.15 C 
B)  0.25 C 
C)  8.8 C 
D)  15 C 
E)  35 C

Question 12

An LC circuit consists of a 1 $\mu$F capacitor and a 4 mH inductor. Its oscillation frequency is approximately:

Accepted Answer

A)  0.025 Hz 
B)  25 Hz 
C)  60 Hz 
D)  2500 Hz 
E)  16,000 Hz 
A)  0.025 Hz 
B)  25 Hz 
C)  60 Hz 
D)  2500 Hz 
E)  16,000 Hz

Question 13

A resistor, an inductor, and a capacitor are connected in parallel to a sinusoidal source of emf. Which of the following is true?

Accepted Answer

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 1/4 cycle. 
D)  The potential difference across the capacitor branch leads the potential difference across the inductor branch by 1/4 cycle. 
E)  The current in the capacitor branch lags the current in the inductor branch by 1/4 cycle. 
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 1/4 cycle. 
D)  The potential difference across the capacitor branch leads the potential difference across the inductor branch by 1/4 cycle. 
E)  The current in the capacitor branch lags the current in the inductor branch by 1/4 cycle.

Question 14

An LC circuit has an inductance of 20 mH and a capacitance of 5.0 $\mu$F. If the charge amplitude is 40 $\mu$C, what is the current amplitude?

Accepted Answer

A)  0.025 A 
B)  0.13 A 
C)  1.0 A 
D)  7.9 A 
E)  400 A 
A)  0.025 A 
B)  0.13 A 
C)  1.0 A 
D)  7.9 A 
E)  400 A

Question 15

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:

Accepted Answer

A)  2 V 
B)  4 V 
C)  12 V 
D)  26 V 
E)  36 V 
A)  2 V 
B)  4 V 
C)  12 V 
D)  26 V 
E)  36 V

Question 16

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:

Accepted Answer

A)  1000 V 
B)  500 V 
C)  250 V 
D)  100 V 
E)  10 V 
A)  1000 V 
B)  500 V 
C)  250 V 
D)  100 V 
E)  10 V

Question 17

In a purely resistive circuit the current:

Accepted Answer

A)  leads the voltage by 1/4 cycle 
B)  leads the voltage by 1/2 cycle 
C)  lags the voltage by 1/4 cycle 
D)  lags the voltage by 1/2 cycle 
E)  is in phase with the voltage 
A)  leads the voltage by 1/4 cycle 
B)  leads the voltage by 1/2 cycle 
C)  lags the voltage by 1/4 cycle 
D)  lags the voltage by 1/2 cycle 
E)  is in phase with the voltage

Question 18

Which of the following has the greatest effect in decreasing the oscillation frequency of an LC circuit? Using instead:

Accepted Answer

A)  L/2 and C/2 
B)  L/2 and 2C 
C)  2L and C/2 
D)  2L and 2C 
E)  none of these 
A)  L/2 and C/2 
B)  L/2 and 2C 
C)  2L and C/2 
D)  2L and 2C 
E)  none of these

Question 19

A power transmission line carries 400A of current at a voltage of 765 kV. If the line has a resistance of 29 µΩ/m, what is the rate at which energy is being dissipated in 800 km of line?

Accepted Answer

A)  0 W 
B)  3.7 kW 
C)  310 kW 
D)  3.7 MW 
E)  310 MW 
A)  0 W 
B)  3.7 kW 
C)  310 kW 
D)  3.7 MW 
E)  310 MW

Question 20

An RLC circuit has a resistance of 200  $\Omega$  an inductance of 15 mH, and a capacitance of 34 nF. At time t = 0 the charge on the capacitor is 25 µC and there is no current flowing. After five complete cycles the energy stored in the capacitor is:

Accepted Answer

A)  0.64 µJ 
B)  77 µJ 
C)  0.49 mJ 
D)  1.8 mJ 
E)  9.2 mJ 
A)  0.64 µJ 
B)  77 µJ 
C)  0.49 mJ 
D)  1.8 mJ 
E)  9.2 mJ

Exam 31: Electromagnetic Oscillations and Alternating Current

The impedance of the circuit shown is:

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 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:

An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- Ω\OmegaΩ resistor, a 400-mH inductor, and a 200- μ\muμ F capacitor. The rms voltage across the resistor is:

The resistance of the primary coil of a well-designed, 1:10 step-down transformer is 1 Ω\OmegaΩ . With the secondary circuit open, the primary is connected to a 12 V ac generator. The primary current is:

An RLC series circuit is driven by a sinusoidal emf with angular frequency ω \omega ω d. If ω \omega ω d 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:

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 sinusoidal voltage V(t) has an rms value of 100 V. Its maximum value is:

A 35- μ\muμ F capacitor is connected to an ac source of emf with a frequency of 400 Hz and a maximum emf of 20 V. The maximum current is:

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:

An LC circuit consists of a 1 μ\muμ F capacitor and a 4 mH inductor. Its oscillation frequency is approximately:

A resistor, an inductor, and a capacitor are connected in parallel to a sinusoidal source of emf. Which of the following is true?

An LC circuit has an inductance of 20 mH and a capacitance of 5.0 μ\muμ F. If the charge amplitude is 40 μ\muμ C, what is the current amplitude?

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 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:

In a purely resistive circuit the current:

Which of the following has the greatest effect in decreasing the oscillation frequency of an LC circuit? Using instead:

A power transmission line carries 400A of current at a voltage of 765 kV. If the line has a resistance of 29 µΩ/m, what is the rate at which energy is being dissipated in 800 km of line?

An RLC circuit has a resistance of 200 Ω\OmegaΩ an inductance of 15 mH, and a capacitance of 34 nF. At time t = 0 the charge on the capacitor is 25 µC and there is no current flowing. After five complete cycles the energy stored in the capacitor is:

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An ac generator producing 10 V (rms) at 200 rad/s is connected in series with a 50- $\Omega$ resistor, a 400-mH inductor, and a 200- $\mu$ F capacitor. The rms voltage across the resistor is:

The resistance of the primary coil of a well-designed, 1:10 step-down transformer is 1 $\Omega$ . With the secondary circuit open, the primary is connected to a 12 V ac generator. The primary current is:

An RLC series circuit is driven by a sinusoidal emf with angular frequency $\omega$ _d. If $\omega$ _d 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:

An RLC series circuit is connected to an oscillator with a maximum emf of 100 V. If the voltage amplitudes V_R, V_L, and V_C are all equal to each other, then V_R must be:

A 35- $\mu$ F capacitor is connected to an ac source of emf with a frequency of 400 Hz and a maximum emf of 20 V. The maximum current is:

An LC circuit consists of a 1 $\mu$ F capacitor and a 4 mH inductor. Its oscillation frequency is approximately:

An LC circuit has an inductance of 20 mH and a capacitance of 5.0 $\mu$ F. If the charge amplitude is 40 $\mu$ C, what is the current amplitude?

An RLC circuit has a resistance of 200 $\Omega$ an inductance of 15 mH, and a capacitance of 34 nF. At time t = 0 the charge on the capacitor is 25 µC and there is no current flowing. After five complete cycles the energy stored in the capacitor is: