Physics: Capacitors, Inductors, and RLC Circuits Worksheet

Question 1

A 12 V battery is connected across a 6.0 microfarad capacitor. How much charge is stored on the capacitor after it is fully charged?

Accepted Answer

The stored charge is 72 microcoulombs. Using Q = CV, Q = (6.0 microfarads)(12 V) = 72 microcoulombs.

Question 2

A capacitor has 0.0030 C of charge stored on it when the voltage across it is 15 V. What is the capacitance?

Accepted Answer

The capacitance is 2.0 x 10^-4 F, or 200 microfarads. Using C = Q/V, C = 0.0030 C / 15 V = 0.00020 F.

Question 3

A 10 microfarad capacitor is charged to 20 V. How much electrical energy is stored in the capacitor?

Accepted Answer

The stored energy is 0.0020 J. Using U = 1/2 CV^2, U = 1/2(10 x 10^-6 F)(20 V)^2 = 0.0020 J.

Question 4

A 1000 ohm resistor is in series with a 220 microfarad capacitor. What is the time constant of the RC circuit?

Accepted Answer

The time constant is 0.22 s. For an RC circuit, tau = RC = (1000 ohms)(220 x 10^-6 F) = 0.22 s.

Question 5

In an RC charging circuit, the time constant is 0.50 s and the battery voltage is 10 V. About what voltage is across the capacitor after one time constant?

Accepted Answer

After one time constant, the capacitor voltage is about 6.3 V. In charging, the capacitor reaches about 63 percent of the final voltage after one time constant, so 0.63 x 10 V = 6.3 V.

Question 6

A 2.0 H inductor carries a current of 3.0 A. How much energy is stored in the magnetic field of the inductor?

Accepted Answer

The stored energy is 9.0 J. Using U = 1/2 LI^2, U = 1/2(2.0 H)(3.0 A)^2 = 9.0 J.

Question 7

A 4.0 H inductor is in series with a 20 ohm resistor. What is the time constant of the RL circuit?

Accepted Answer

The time constant is 0.20 s. For an RL circuit, tau = L/R = 4.0 H / 20 ohms = 0.20 s.

Question 8

An AC source has a frequency of 60 Hz and is connected to a 50 microfarad capacitor. What is the capacitive reactance?

Accepted Answer

The capacitive reactance is about 53 ohms. Using XC = 1/(2 pi f C), XC = 1/(2 pi)(60 Hz)(50 x 10^-6 F) = 53 ohms.

Question 9

An AC source has a frequency of 400 Hz and is connected to a 0.25 H inductor. What is the inductive reactance?

Accepted Answer

The inductive reactance is about 628 ohms. Using XL = 2 pi f L, XL = (2 pi)(400 Hz)(0.25 H) = 628 ohms.

Question 10

A series RLC circuit has R = 30 ohms, XL = 80 ohms, and XC = 40 ohms. What is the impedance of the circuit?

Accepted Answer

The impedance is 50 ohms. The net reactance is XL - XC = 80 ohms - 40 ohms = 40 ohms, so Z = sqrt(R^2 + (XL - XC)^2) = sqrt(30^2 + 40^2) = 50 ohms.

Question 11

A series RLC circuit has a 0.50 H inductor and a 20 microfarad capacitor. What is the resonant frequency of the circuit?

Accepted Answer

The resonant frequency is about 50 Hz. Using f0 = 1/(2 pi sqrt(LC)), f0 = 1/(2 pi sqrt((0.50 H)(20 x 10^-6 F))) = about 50 Hz.

Question 12

A graph shows current versus frequency for a series RLC circuit. The current reaches its maximum value at 120 Hz. What is the resonant frequency, and what happens to the impedance at that frequency?

Accepted Answer

The resonant frequency is 120 Hz. At resonance in a series RLC circuit, the impedance is at its minimum value because the inductive and capacitive reactances cancel each other.

Physics: Capacitors, Inductors, and RLC Circuits

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