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 = 100 nF+−10 VL = 100 mHiL​

A 100 nF capacitor charged to 10 V is switched across an ideal 100 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 100 nFV0 = 10 VL = 100 mH
Imax = mA
2.Easy
C = 4.7 nFL = 22 mH

An ideal LC circuit has L = 22 mH and C = 4.7 nF. Find its natural (resonance) frequency f0 in kHz.

L = 22 mHC = 4.7 nF
f0 = kHz
3.Medium
V47 kΩ47 mH10 nF

A parallel RLC circuit has R = 47 kΩ, L = 47 mH and C = 10 nF. Find its quality factor Q.

R = 47 kΩL = 47 mHC = 10 nF
Q =
4.Medium
V22 Ω47 mH22 nF

A series RLC circuit has R = 22 Ω, L = 47 mH and C = 22 nF. Find its bandwidth BW in Hz.

R = 22 ΩL = 47 mHC = 22 nF
BW = Hz
5.Hard
V10 Ω4.7 mH100 nF10 mA

A series RLC circuit (R = 10 Ω, L = 4.7 mH, C = 100 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 10 ΩL = 4.7 mHC = 100 nFIm = 10 mA
Ecycle = nJ
6.Hard
f|I|0.7071f0​ = ?100 kHz250 kHzBW

The half-power frequencies of a resonance curve are 100 kHz and 250 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 100 kHzf2 = 250 kHz
Q =

Answer key

  1. 1. Imax = 10 mA
  2. 2. f0 = 15.65 kHz
  3. 3. Q = 21.68
  4. 4. BW = 74.5 Hz
  5. 5. Ecycle = 68.11 nJ
  6. 6. Q = 1.054

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