LC resonance, Q factor & bandwidth worksheet with answers

Free printable LC resonance, Q factor & bandwidth worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A tuned circuit resonates at 1.6 MHz and has a quality factor Q = 40. Find its bandwidth BW in kHz.

f₀ = 1.6 MHzQ = 40

BW = kHz

2.Easy

A tuned circuit resonates at 2 kHz and has a quality factor Q = 40. Find its bandwidth BW in Hz.

f₀ = 2 kHzQ = 40

BW = Hz

3.Medium

A 47 nF capacitor charged to 15 V oscillates with an ideal 1 mH inductor. Find the energy W_L stored in the inductor at the moment the capacitor voltage is 3 V, in µJ.

C = 47 nFV₀ = 15 Vv_C = 3 V

W_L = µJ

4.Medium

In an ideal LC circuit with L = 2.2 mH and C = 22 nF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 2.2 mHC = 22 nF

t = µs

5.Hard

The half-power frequencies of a resonance curve are 8 kHz and 10 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f₁ = 8 kHzf₂ = 10 kHz

Q =

6.Hard

A charged 47 nF capacitor discharges through a 470 µH coil with a total series resistance of 1 Ω, so the oscillation slowly dies out. Its amplitude decays as e^−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 470 µHC = 47 nFR = 1 Ω

n =

Answer key

1. BW = 40 kHz
2. BW = 50 Hz
3. W_L = 5.076 µJ
4. t = 10.93 µs
5. Q = 4.472
6. n = 22.06

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