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 = 4.7 mH

An LC circuit with L = 4.7 mH must resonate at 50 kHz. Find the capacitance C in nF.

L = 4.7 mHf0 = 50 kHz
C = nF
2.Easy
f|I|0.70711 MHzf1​f2​BW = ?

A tuned circuit resonates at 1 MHz and has a quality factor Q = 10. Find its bandwidth BW in kHz.

f0 = 1 MHzQ = 10
BW = kHz
3.Medium
V4.7 kΩ10 mH220 nF

A parallel RLC circuit has R = 4.7 kΩ, L = 10 mH and C = 220 nF. Find its quality factor Q.

R = 4.7 kΩL = 10 mHC = 220 nF
Q =
4.Medium
V47 Ω470 µH2.2 nF

A series RLC circuit has R = 47 Ω, L = 470 µH and C = 2.2 nF. Find its bandwidth BW in kHz.

R = 47 ΩL = 470 µHC = 2.2 nF
BW = kHz
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 10 kHz and a bandwidth of 500 Hz. Find the capacitance C in nF.

R = 20 Ωf0 = 10 kHzBW = 500 Hz
C = nF
6.Hard
f|I|0.7071f0​ = ?100 kHz125 kHzBW

The half-power frequencies of a resonance curve are 100 kHz and 125 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 100 kHzf2 = 125 kHz
Q =

Answer key

  1. 1. C = 2.156 nF
  2. 2. BW = 100 kHz
  3. 3. Q = 22.04
  4. 4. BW = 15.92 kHz
  5. 5. C = 39.79 nF
  6. 6. Q = 4.472

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