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

An ideal LC circuit has L = 1 mH and C = 100 nF. Find its natural (resonance) frequency f₀ in kHz.

L = 1 mHC = 100 nF

f₀ = kHz

2.Easy

A 100 nF capacitor is charged to 12 V and then connected to an ideal 220 µH inductor. Find the total energy W that swings between them, in µJ.

C = 100 nFV₀ = 12 VL = 220 µH

W = µJ

3.Medium

In an ideal LC circuit with L = 100 mH and C = 10 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 = 100 mHC = 10 nF

t = µs

4.Medium

A series RLC circuit resonates at 200 kHz with Q = 3. Find the lower half-power frequency f₁ exactly, in kHz.

f₀ = 200 kHzQ = 3

f₁ = kHz

5.Hard

The half-power frequencies of a resonance curve are 8 kHz and 20 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f₁ = 8 kHzf₂ = 20 kHz

Q =

6.Hard

A charged 2.2 nF capacitor discharges through a 470 µH coil with a total series resistance of 20 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 = 2.2 nFR = 20 Ω

n =

Answer key

1. f₀ = 15.92 kHz
2. W = 7.2 µJ
3. t = 49.67 µs
4. f₁ = 169.4 kHz
5. Q = 1.054
6. n = 5.099

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