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 nF+−10 VL = 47 µHiL​

A 470 nF capacitor charged to 10 V is switched across an ideal 47 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 470 nFV0 = 10 VL = 47 µH
Imax = mA
2.Easy
C = ?L = 47 µH

An LC circuit with L = 47 µH must resonate at 1 MHz. Find the capacitance C in nF.

L = 47 µHf0 = 1 MHz
C = nF
3.Medium
V220 Ω10 mH47 nF

A series RLC circuit has R = 220 Ω, L = 10 mH and C = 47 nF. Find its quality factor Q.

R = 220 ΩL = 10 mHC = 47 nF
Q =
4.Medium
V220 Ω47 mH100 pF

A series RLC circuit has R = 220 Ω, L = 47 mH and C = 100 pF. Find its bandwidth BW in Hz.

R = 220 ΩL = 47 mHC = 100 pF
BW = Hz
5.Hard
VR = ?1 mHC

A series resonant circuit uses a 1 mH inductor. Which total series resistance R gives a bandwidth of 10 kHz?

L = 1 mHBW = 10 kHz
R = Ω
6.Hard
f|I|0.7071f0​ = ?100 kHz200 kHzBW

The half-power frequencies of a resonance curve are 100 kHz and 200 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 100 kHzf2 = 200 kHz
Q =

Answer key

  1. 1. Imax = 1000 mA
  2. 2. C = 0.5389 nF
  3. 3. Q = 2.097
  4. 4. BW = 745 Hz
  5. 5. R = 62.83 Ω
  6. 6. Q = 1.414

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