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 kHzf1​f2​BW = 100 Hz

A resonance curve peaks at 10 kHz, and its half-power points are 100 Hz apart. Find the quality factor Q.

f0 = 10 kHzBW = 100 Hz
Q =
2.Easy
C = 47 nF+−3 VL = 22 µHiL​

A 47 nF capacitor charged to 3 V is switched across an ideal 22 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 47 nFV0 = 3 VL = 22 µH
Imax = mA
3.Medium
V1 Ω10 µH47 nF

A series RLC circuit has R = 1 Ω, L = 10 µH and C = 47 nF. Find its bandwidth BW in kHz.

R = 1 ΩL = 10 µHC = 47 nF
BW = kHz
4.Medium
f|I|0.70712 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 2 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 2 kHzQ = 3
f1 = kHz
5.Hard
f|I|0.7071f0​ = ?50 kHz62.5 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 62.5 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 62.5 kHz
Q =
6.Hard
VR = ?100 µHC

A series resonant circuit uses a 100 µH inductor. Which total series resistance R gives a bandwidth of 100 kHz?

L = 100 µHBW = 100 kHz
R = Ω

Answer key

  1. 1. Q = 100
  2. 2. Imax = 138.7 mA
  3. 3. BW = 15.92 kHz
  4. 4. f1 = 1.694 kHz
  5. 5. Q = 4.472
  6. 6. R = 62.83 Ω

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