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 = 2.2 mH

An LC circuit with L = 2.2 mH must resonate at 10 kHz. Find the capacitance C in nF.

L = 2.2 mHf0 = 10 kHz
C = nF
2.Easy
f|I|0.707110 kHzf1​f2​BW = ?

A tuned circuit resonates at 10 kHz and has a quality factor Q = 40. Find its bandwidth BW in Hz.

f0 = 10 kHzQ = 40
BW = Hz
3.Medium
V47 kΩ47 mH220 nF

A parallel RLC circuit has R = 47 kΩ, L = 47 mH and C = 220 nF. Find its quality factor Q.

R = 47 kΩL = 47 mHC = 220 nF
Q =
4.Medium
f|I|0.7071200 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 200 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 200 kHzQ = 1.5
f1 = kHz
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 50 kHz and a bandwidth of 2 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 50 kHzBW = 2 kHz
C = nF
6.Hard
VR = ?470 µHC

A series resonant circuit uses a 470 µH inductor. Which total series resistance R gives a bandwidth of 5 kHz?

L = 470 µHBW = 5 kHz
R = Ω

Answer key

  1. 1. C = 115.1 nF
  2. 2. BW = 250 Hz
  3. 3. Q = 101.7
  4. 4. f1 = 144.2 kHz
  5. 5. C = 6.366 nF
  6. 6. R = 14.77 Ω

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