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 1 µF capacitor is charged to 12 V and then connected to an ideal 22 µH inductor. Find the total energy W that swings between them, in µJ.

C = 1 µFV₀ = 12 VL = 22 µH

W = µJ

2.Easy

A 2.2 µF capacitor is charged to 9 V and then connected to an ideal 2.2 µH inductor. Find the total energy W that swings between them, in µJ.

C = 2.2 µFV₀ = 9 VL = 2.2 µH

W = µJ

3.Medium

In an ideal LC circuit with L = 470 µH and C = 220 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 = 470 µHC = 220 nF

t = µs

4.Medium

A series RLC circuit has R = 5 Ω, L = 470 µH and C = 4.7 nF. Find its quality factor Q.

R = 5 ΩL = 470 µHC = 4.7 nF

Q =

5.Hard

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 100 kHz and a bandwidth of 2 kHz. Find the capacitance C in nF.

R = 5 Ωf₀ = 100 kHzBW = 2 kHz

C = nF

6.Hard

A charged 100 nF capacitor discharges through a 2.2 mH coil with a total series resistance of 10 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 = 100 nFR = 10 Ω

n =

Answer key

1. W = 72 µJ
2. W = 89.1 µJ
3. t = 15.97 µs
4. Q = 63.25
5. C = 6.366 nF
6. n = 3.273

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