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 47 nF capacitor charged to 3 V is switched across an ideal 2.2 mH inductor. Find the peak current I_max in the circuit, in mA.

C = 47 nFV₀ = 3 VL = 2.2 mH

I_max = mA

2.Easy

A tuned circuit resonates at 10 kHz and has a quality factor Q = 5. Find its bandwidth BW in kHz.

f₀ = 10 kHzQ = 5

BW = kHz

3.Medium

A 100 nF capacitor charged to 15 V oscillates with an ideal 22 µH inductor. Find the energy W_L stored in the inductor at the moment the capacitor voltage is 6 V, in µJ.

C = 100 nFV₀ = 15 Vv_C = 6 V

W_L = µJ

4.Medium

A series RLC circuit resonates at 500 kHz with Q = 5. Find the lower half-power frequency f₁ exactly, in kHz.

f₀ = 500 kHzQ = 5

f₁ = kHz

5.Hard

A charged 10 nF capacitor discharges through a 10 µH coil with a total series resistance of 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 = 10 µHC = 10 nFR = 5 Ω

n =

6.Hard

A series RLC circuit (R = 5 Ω, L = 47 mH, C = 100 nF) is driven at resonance with a current amplitude of 20 mA. Find the energy E_cycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 47 mHC = 100 nFI_m = 20 mA

E_cycle = nJ

Answer key

1. I_max = 13.87 mA
2. BW = 2 kHz
3. W_L = 9.45 µJ
4. f₁ = 452.5 kHz
5. n = 1.395
6. E_cycle = 430.8 nJ

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