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
tvC​iL​T/4T/2TV0​ = 20 VC = 47 nF

A 47 nF capacitor is charged to 20 V and then connected to an ideal 0.47 µH inductor. Find the total energy W that swings between them, in µJ.

C = 47 nFV0 = 20 VL = 0.47 µH
W = µJ
2.Easy
tvC​iL​T/4T/2TV0​ = 3 VC = 1 µF

A 1 µF capacitor is charged to 3 V and then connected to an ideal 4.7 mH inductor. Find the total energy W that swings between them, in µJ.

C = 1 µFV0 = 3 VL = 4.7 mH
W = µJ
3.Medium
f|I|0.70712 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 2 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 2 kHzQ = 1.5
f1 = kHz
4.Medium
f|I|0.707110 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 10 kHz with Q = 2.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 10 kHzQ = 2.5
f1 = kHz
5.Hard
f|I|0.7071f0​ = ?20 kHz25 kHzBW

The half-power frequencies of a resonance curve are 20 kHz and 25 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 20 kHzf2 = 25 kHz
Q =
6.Hard
C = 100 nFr = 20 ΩL = 4.7 mH

A parallel tank circuit is made of a 100 nF capacitor and a 4.7 mH coil with a winding resistance of 20 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 4.7 mHC = 100 nFr = 20 Ω
RD = kΩ

Answer key

  1. 1. W = 9.4 µJ
  2. 2. W = 4.5 µJ
  3. 3. f1 = 1.442 kHz
  4. 4. f1 = 8.198 kHz
  5. 5. Q = 4.472
  6. 6. RD = 2.35 kΩ

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