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
C = ?L = 1 mH

An LC circuit with L = 1 mH must resonate at 500 kHz. Find the capacitance C in nF.

L = 1 mHf0 = 500 kHz
C = nF
2.Easy
C = 470 pF+−2 VL = 220 µHiL​

A 470 pF capacitor charged to 2 V is switched across an ideal 220 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 470 pFV0 = 2 VL = 220 µH
Imax = mA
3.Medium
V1 Ω220 µH1 µF

A series RLC circuit has R = 1 Ω, L = 220 µH and C = 1 µF. Find its quality factor Q.

R = 1 ΩL = 220 µHC = 1 µF
Q =
4.Medium
V220 Ω47 mH220 nF

A series RLC circuit has R = 220 Ω, L = 47 mH and C = 220 nF. Find its bandwidth BW in Hz.

R = 220 ΩL = 47 mHC = 220 nF
BW = Hz
5.Hard
V22 Ω22 mH10 nF200 mA

A series RLC circuit (R = 22 Ω, L = 22 mH, C = 10 nF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 22 ΩL = 22 mHC = 10 nFIm = 200 mA
Ecycle = µJ
6.Hard
f|I|0.7071f0​ = ?2 kHz5 kHzBW

The half-power frequencies of a resonance curve are 2 kHz and 5 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 2 kHzf2 = 5 kHz
Q =

Answer key

  1. 1. C = 0.1013 nF
  2. 2. Imax = 2.923 mA
  3. 3. Q = 14.83
  4. 4. BW = 745 Hz
  5. 5. Ecycle = 41.01 µJ
  6. 6. Q = 1.054

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