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 ideal LC circuit has L = 100 mH and C = 47 pF. Find its natural (resonance) frequency f₀ in kHz.

L = 100 mHC = 47 pF

f₀ = kHz

2.Easy

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 20. Find its bandwidth BW in kHz.

f₀ = 10.7 MHzQ = 20

BW = kHz

3.Medium

A 1 µF capacitor charged to 15 V oscillates with an ideal 220 µH inductor. Find the energy W_L stored in the inductor at the moment the capacitor voltage is 9 V, in µJ.

C = 1 µFV₀ = 15 Vv_C = 9 V

W_L = µJ

4.Medium

A 2.2 nF capacitor charged to 20 V oscillates with an ideal 1 mH inductor. Find the energy W_L stored in the inductor at the moment the capacitor voltage is 16 V, in nJ.

C = 2.2 nFV₀ = 20 Vv_C = 16 V

W_L = nJ

5.Hard

A charged 2.2 µF capacitor discharges through a 4.7 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 = 4.7 mHC = 2.2 µFR = 2 Ω

n =

6.Hard

A parallel tank circuit is made of a 4.7 nF capacitor and a 100 mH coil with a winding resistance of 10 Ω. At resonance it behaves like a resistor, its dynamic resistance R_D = L/(C·r). Find R_D in kΩ.

L = 100 mHC = 4.7 nFr = 10 Ω

R_D = kΩ

Answer key

1. f₀ = 73.41 kHz
2. BW = 535 kHz
3. W_L = 72 µJ
4. W_L = 158.4 nJ
5. n = 5.099
6. R_D = 2128 kΩ

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