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|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 20. Find its bandwidth BW in kHz.

f0 = 10.7 MHzQ = 20
BW = kHz
2.Easy
C = ?L = 22 µH

An LC circuit with L = 22 µH must resonate at 50 kHz. Find the capacitance C in nF.

L = 22 µHf0 = 50 kHz
C = nF
3.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

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

f0 = 5 kHzQ = 5
f1 = kHz
4.Medium
V10 Ω470 µH220 nF

A series RLC circuit has R = 10 Ω, L = 470 µH and C = 220 nF. Find its bandwidth BW in kHz.

R = 10 ΩL = 470 µHC = 220 nF
BW = kHz
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 100 kHz and a bandwidth of 4 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 100 kHzBW = 4 kHz
C = nF
6.Hard
f|I|0.7071f0​ = ?5 kHz6 kHzBW

The half-power frequencies of a resonance curve are 5 kHz and 6 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 5 kHzf2 = 6 kHz
Q =

Answer key

  1. 1. BW = 535 kHz
  2. 2. C = 460.6 nF
  3. 3. f1 = 4.525 kHz
  4. 4. BW = 3.386 kHz
  5. 5. C = 3.183 nF
  6. 6. Q = 5.477

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