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 5 kHz and has a quality factor Q = 80. Find its bandwidth BW in Hz.

f₀ = 5 kHzQ = 80

BW = Hz

2.Easy

A 470 pF capacitor is charged to 6 V and then connected to an ideal 1 mH inductor. Find the total energy W that swings between them, in nJ.

C = 470 pFV₀ = 6 VL = 1 mH

W = nJ

3.Medium

A parallel RLC circuit has R = 1 kΩ, L = 4.7 mH and C = 100 nF. Find its quality factor Q.

R = 1 kΩL = 4.7 mHC = 100 nF

Q =

4.Medium

In an ideal LC circuit with L = 100 mH 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 = 100 mHC = 220 nF

t = µs

5.Hard

A charged 220 nF capacitor discharges through a 47 µH 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 = 47 µHC = 220 nFR = 0.5 Ω

n =

6.Hard

A series RLC circuit (R = 10 Ω, L = 100 µH, C = 10 nF) is driven at resonance with a current amplitude of 50 mA. Find the energy E_cycle dissipated in R during one cycle, in nJ.

R = 10 ΩL = 100 µHC = 10 nFI_m = 50 mA

E_cycle = nJ

Answer key

1. BW = 62.5 Hz
2. W = 8.46 nJ
3. Q = 4.613
4. t = 233 µs
5. n = 6.45
6. E_cycle = 78.54 nJ

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