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 20 kHz. Find the capacitance C in nF.

L = 2.2 mHf0 = 20 kHz
C = nF
2.Easy
f|I|0.70711.6 MHzf1​f2​BW = 160 kHz

A resonance curve peaks at 1.6 MHz, and its half-power points are 160 kHz apart. Find the quality factor Q.

f0 = 1.6 MHzBW = 160 kHz
Q =
3.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 5 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 5 kHzQ = 2
f1 = kHz
4.Medium
V2.2 kΩ1 mH4.7 nF

A parallel RLC circuit has R = 2.2 kΩ, L = 1 mH and C = 4.7 nF. Find its quality factor Q.

R = 2.2 kΩL = 1 mHC = 4.7 nF
Q =
5.Hard
f|I|0.7071f0​ = ?1 kHz1.6 kHzBW

The half-power frequencies of a resonance curve are 1 kHz and 1.6 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 1 kHzf2 = 1.6 kHz
Q =
6.Hard
V2 Ω2.2 mH1 µF200 mA

A series RLC circuit (R = 2 Ω, L = 2.2 mH, C = 1 µF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 2 ΩL = 2.2 mHC = 1 µFIm = 200 mA
Ecycle = µJ

Answer key

  1. 1. C = 28.78 nF
  2. 2. Q = 10
  3. 3. f1 = 3.904 kHz
  4. 4. Q = 4.769
  5. 5. Q = 2.108
  6. 6. Ecycle = 11.79 µJ

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