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 = 100 pFL = 47 mH

An ideal LC circuit has L = 47 mH and C = 100 pF. Find its natural (resonance) frequency f0 in kHz.

L = 47 mHC = 100 pF
f0 = kHz
2.Easy
C = ?L = 470 µH

An LC circuit with L = 470 µH must resonate at 10 kHz. Find the capacitance C in nF.

L = 470 µHf0 = 10 kHz
C = nF
3.Medium
V10 Ω470 µH1 µF

A series RLC circuit has R = 10 Ω, L = 470 µH and C = 1 µF. Find its quality factor Q.

R = 10 ΩL = 470 µHC = 1 µF
Q =
4.Medium
V47 Ω1 mH470 pF

A series RLC circuit has R = 47 Ω, L = 1 mH and C = 470 pF. Find its bandwidth BW in kHz.

R = 47 ΩL = 1 mHC = 470 pF
BW = kHz
5.Hard
f|I|0.7071f0​ = ?1 kHz1.05 kHzBW

The half-power frequencies of a resonance curve are 1 kHz and 1.05 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 1 kHzf2 = 1.05 kHz
Q =
6.Hard
C = 2.2 nFr = 20 ΩL = 2.2 mH

A parallel tank circuit is made of a 2.2 nF capacitor and a 2.2 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 = 2.2 mHC = 2.2 nFr = 20 Ω
RD = kΩ

Answer key

  1. 1. f0 = 73.41 kHz
  2. 2. C = 538.9 nF
  3. 3. Q = 2.168
  4. 4. BW = 7.48 kHz
  5. 5. Q = 20.49
  6. 6. RD = 50 kΩ

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