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 resonance curve peaks at 10 kHz, and its half-power points are 400 Hz apart. Find the quality factor Q.

f₀ = 10 kHzBW = 400 Hz

Q =

2.Easy

An ideal LC circuit has L = 470 µH and C = 100 nF. Find its natural (resonance) frequency f₀ in kHz.

L = 470 µHC = 100 nF

f₀ = kHz

3.Medium

In an ideal LC circuit with L = 470 µH and C = 47 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 = 47 nF

t = µs

4.Medium

A series RLC circuit has R = 1 Ω, L = 1 mH and C = 47 nF. Find its bandwidth BW in Hz.

R = 1 ΩL = 1 mHC = 47 nF

BW = Hz

5.Hard

A charged 2.2 µF 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 = 2.2 µFR = 1 Ω

n =

6.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 =

Answer key

1. Q = 25
2. f₀ = 23.22 kHz
3. t = 7.383 µs
4. BW = 159.2 Hz
5. n = 1.488
6. n = 6.45

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