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 = 80. Find its bandwidth BW in kHz.

f₀ = 1.6 MHzQ = 80

BW = kHz

2.Easy

An ideal LC circuit has L = 4.7 mH and C = 1 nF. Find its natural (resonance) frequency f₀ in kHz.

L = 4.7 mHC = 1 nF

f₀ = kHz

3.Medium

In an ideal LC circuit with L = 22 mH and C = 470 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 = 22 mHC = 470 nF

t = µs

4.Medium

In an ideal LC circuit with L = 22 µH and C = 1 µF, 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 = 22 µHC = 1 µF

t = µs

5.Hard

The half-power frequencies of a resonance curve are 10 kHz and 16 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f₁ = 10 kHzf₂ = 16 kHz

Q =

6.Hard

A charged 10 µF capacitor discharges through a 2.2 mH coil with a total series resistance of 0.5 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 = 2.2 mHC = 10 µFR = 0.5 Ω

n =

Answer key

1. BW = 20 kHz
2. f₀ = 73.41 kHz
3. t = 159.7 µs
4. t = 7.368 µs
5. Q = 2.108
6. n = 6.545

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