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 = 47 nF+−2 VL = 47 µHiL​

A 47 nF capacitor charged to 2 V is switched across an ideal 47 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 47 nFV0 = 2 VL = 47 µH
Imax = mA
2.Easy
C = ?L = 22 mH

An LC circuit with L = 22 mH must resonate at 20 kHz. Find the capacitance C in nF.

L = 22 mHf0 = 20 kHz
C = nF
3.Medium
V10 Ω22 mH220 nF

A series RLC circuit has R = 10 Ω, L = 22 mH and C = 220 nF. Find its bandwidth BW in Hz.

R = 10 ΩL = 22 mHC = 220 nF
BW = Hz
4.Medium
f|I|0.707120 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 20 kHz with Q = 2.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 20 kHzQ = 2.5
f1 = kHz
5.Hard
VR = ?22 mHC

A series resonant circuit uses a 22 mH inductor. Which total series resistance R gives a bandwidth of 20 kHz?

L = 22 mHBW = 20 kHz
R = Ω
6.Hard
f|I|0.7071f0​ = ?50 kHz75 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 75 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 75 kHz
Q =

Answer key

  1. 1. Imax = 63.25 mA
  2. 2. C = 2.878 nF
  3. 3. BW = 72.34 Hz
  4. 4. f1 = 16.4 kHz
  5. 5. R = 2765 Ω
  6. 6. Q = 2.449

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