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 pF+−2 VL = 220 µHiL​

A 470 pF capacitor charged to 2 V is switched across an ideal 220 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 470 pFV0 = 2 VL = 220 µH
Imax = mA
2.Easy
f|I|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 20. Find its bandwidth BW in kHz.

f0 = 10.7 MHzQ = 20
BW = kHz
3.Medium
V100 Ω220 µH4.7 nF

A series RLC circuit has R = 100 Ω, L = 220 µH and C = 4.7 nF. Find its quality factor Q.

R = 100 ΩL = 220 µHC = 4.7 nF
Q =
4.Medium
V100 Ω4.7 mH100 pF

A series RLC circuit has R = 100 Ω, L = 4.7 mH and C = 100 pF. Find its bandwidth BW in kHz.

R = 100 ΩL = 4.7 mHC = 100 pF
BW = kHz
5.Hard
VR = ?22 µHC

A series resonant circuit uses a 22 µH inductor. Which total series resistance R gives a bandwidth of 10 kHz?

L = 22 µHBW = 10 kHz
R = Ω
6.Hard
f|I|0.7071f0​ = ?400 kHz480 kHzBW

The half-power frequencies of a resonance curve are 400 kHz and 480 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 400 kHzf2 = 480 kHz
Q =

Answer key

  1. 1. Imax = 2.923 mA
  2. 2. BW = 535 kHz
  3. 3. Q = 2.164
  4. 4. BW = 3.386 kHz
  5. 5. R = 1.382 Ω
  6. 6. Q = 5.477

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