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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

An LC circuit with L = 47 mH must resonate at 5 kHz. Find the capacitance C in nF.

L = 47 mHf₀ = 5 kHz

C = nF

2.Easy

A 220 nF capacitor is charged to 24 V and then connected to an ideal 22 µH inductor. Find the total energy W that swings between them, in µJ.

C = 220 nFV₀ = 24 VL = 22 µH

W = µJ

3.Medium

In an ideal LC circuit with L = 0.47 µH and C = 100 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 = 0.47 µHC = 100 nF

t = µs

4.Medium

In an ideal LC circuit with L = 47 µH and C = 4.7 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 = 47 µHC = 4.7 nF

t = µs

5.Hard

A charged 1 µF capacitor discharges through a 22 mH 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 = 22 mHC = 1 µFR = 1 Ω

n =

6.Hard

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 10 kHz and a bandwidth of 200 Hz. Find the capacitance C in nF.

R = 20 Ωf₀ = 10 kHzBW = 200 Hz

C = nF

Answer key

1. C = 21.56 nF
2. W = 63.36 µJ
3. t = 0.3405 µs
4. t = 0.7383 µs
5. n = 32.73
6. C = 15.92 nF

Full step-by-step solutions: practise this topic on examproblems.com.