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 LC circuit with L = 47 mH must resonate at 200 kHz. Find the capacitance C in nF.

L = 47 mHf₀ = 200 kHz

C = nF

2.Easy

A resonance curve peaks at 50 kHz, and its half-power points are 2 kHz apart. Find the quality factor Q.

f₀ = 50 kHzBW = 2 kHz

Q =

3.Medium

A 2.2 µF 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 7.5 V, in µJ.

C = 2.2 µFV₀ = 15 Vv_C = 7.5 V

W_L = µJ

4.Medium

A 10 pF capacitor charged to 5 V oscillates with an ideal 10 mH inductor. Find the energy W_L stored in the inductor at the moment the capacitor voltage is 2.5 V, in nJ.

C = 10 pFV₀ = 5 Vv_C = 2.5 V

W_L = nJ

5.Hard

A charged 470 nF capacitor discharges through a 1 mH coil with a total series resistance of 2 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 = 1 mHC = 470 nFR = 2 Ω

n =

6.Hard

A charged 470 nF capacitor discharges through a 100 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 = 100 µHC = 470 nFR = 1 Ω

n =

Answer key

1. C = 0.01347 nF
2. Q = 25
3. W_L = 185.6 µJ
4. W_L = 0.09375 nJ
5. n = 5.089
6. n = 3.218

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