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|0.7071500 kHzf1​f2​BW = 41.67 kHz

A resonance curve peaks at 500 kHz, and its half-power points are 41.67 kHz apart. Find the quality factor Q.

f0 = 500 kHzBW = 41.67 kHz
Q =
2.Easy
C = 47 nF+−6 VL = 4.7 mHiL​

A 47 nF capacitor charged to 6 V is switched across an ideal 4.7 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 47 nFV0 = 6 VL = 4.7 mH
Imax = mA
3.Medium
V220 Ω2.2 mH10 nF

A series RLC circuit has R = 220 Ω, L = 2.2 mH and C = 10 nF. Find its bandwidth BW in kHz.

R = 220 ΩL = 2.2 mHC = 10 nF
BW = kHz
4.Medium
V100 Ω100 µH2.2 nF

A series RLC circuit has R = 100 Ω, L = 100 µH and C = 2.2 nF. Find its bandwidth BW in kHz.

R = 100 ΩL = 100 µHC = 2.2 nF
BW = kHz
5.Hard
f|I|0.7071f0​ = ?2 kHz2.4 kHzBW

The half-power frequencies of a resonance curve are 2 kHz and 2.4 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 2 kHzf2 = 2.4 kHz
Q =
6.Hard
VR = ?1 mHC

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

L = 1 mHBW = 1 kHz
R = Ω

Answer key

  1. 1. Q = 12
  2. 2. Imax = 18.97 mA
  3. 3. BW = 15.92 kHz
  4. 4. BW = 159.2 kHz
  5. 5. Q = 5.477
  6. 6. R = 6.283 Ω

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