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 = 220 nF+−15 VL = 100 mHiL​

A 220 nF capacitor charged to 15 V is switched across an ideal 100 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 220 nFV0 = 15 VL = 100 mH
Imax = mA
2.Easy
tvC​iL​T/4T/2TV0​ = 2 VC = 1 µF

A 1 µF capacitor is charged to 2 V and then connected to an ideal 220 µH inductor. Find the total energy W that swings between them, in µJ.

C = 1 µFV0 = 2 VL = 220 µH
W = µJ
3.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 5 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 5 kHzQ = 2
f1 = kHz
4.Medium
V5 Ω47 µH47 nF

A series RLC circuit has R = 5 Ω, L = 47 µH and C = 47 nF. Find its bandwidth BW in kHz.

R = 5 ΩL = 47 µHC = 47 nF
BW = kHz
5.Hard
V1 Ω22 µH2.2 µF500 mA

A series RLC circuit (R = 1 Ω, L = 22 µH, C = 2.2 µF) is driven at resonance with a current amplitude of 500 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 1 ΩL = 22 µHC = 2.2 µFIm = 500 mA
Ecycle = µJ
6.Hard
f|I|0.7071f0​ = ?10 kHz10.5 kHzBW

The half-power frequencies of a resonance curve are 10 kHz and 10.5 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 10 kHzf2 = 10.5 kHz
Q =

Answer key

  1. 1. Imax = 22.25 mA
  2. 2. W = 2 µJ
  3. 3. f1 = 3.904 kHz
  4. 4. BW = 16.93 kHz
  5. 5. Ecycle = 5.464 µJ
  6. 6. Q = 20.49

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