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
f|I|0.7071500 kHzf1​f2​BW = 6.25 kHz

A resonance curve peaks at 500 kHz, and its half-power points are 6.25 kHz apart. Find the quality factor Q.

f0 = 500 kHzBW = 6.25 kHz
Q =
2.Easy
C = ?L = 100 mH

An LC circuit with L = 100 mH must resonate at 20 kHz. Find the capacitance C in nF.

L = 100 mHf0 = 20 kHz
C = nF
3.Medium
V10 Ω10 mH220 nF

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

R = 10 ΩL = 10 mHC = 220 nF
BW = Hz
4.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 5 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 5 kHzQ = 3
f1 = kHz
5.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 =
6.Hard
VR = ?22 µHC

A series resonant circuit uses a 22 µH inductor. Which total series resistance R gives a bandwidth of 1 kHz?

L = 22 µHBW = 1 kHz
R = Ω

Answer key

  1. 1. Q = 80
  2. 2. C = 0.6333 nF
  3. 3. BW = 159.2 Hz
  4. 4. f1 = 4.236 kHz
  5. 5. Q = 20.49
  6. 6. R = 0.1382 Ω

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