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 = 470 pFL = 47 µH

An ideal LC circuit has L = 47 µH and C = 470 pF. Find its natural (resonance) frequency f0 in MHz.

L = 47 µHC = 470 pF
f0 = MHz
2.Easy
C = ?L = 0.47 µH

An LC circuit with L = 0.47 µH must resonate at 1 MHz. Find the capacitance C in nF.

L = 0.47 µHf0 = 1 MHz
C = nF
3.Medium
V1 kΩ4.7 mH470 nF

A parallel RLC circuit has R = 1 kΩ, L = 4.7 mH and C = 470 nF. Find its quality factor Q.

R = 1 kΩL = 4.7 mHC = 470 nF
Q =
4.Medium
V47 Ω10 mH220 pF

A series RLC circuit has R = 47 Ω, L = 10 mH and C = 220 pF. Find its bandwidth BW in Hz.

R = 47 ΩL = 10 mHC = 220 pF
BW = Hz
5.Hard
f|I|0.7071f0​ = ?8 kHz8.4 kHzBW

The half-power frequencies of a resonance curve are 8 kHz and 8.4 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 8 kHzf2 = 8.4 kHz
Q =
6.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 500 kHz and a bandwidth of 50 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 500 kHzBW = 50 kHz
C = nF

Answer key

  1. 1. f0 = 1.071 MHz
  2. 2. C = 53.89 nF
  3. 3. Q = 10
  4. 4. BW = 748 Hz
  5. 5. Q = 20.49
  6. 6. C = 0.6366 nF

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