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 pFL = 220 µH

An ideal LC circuit has L = 220 µH and C = 470 pF. Find its natural (resonance) frequency f0 in kHz.

L = 220 µHC = 470 pF
f0 = kHz
2.Easy
C = ?L = 100 µH

An LC circuit with L = 100 µH must resonate at 100 kHz. Find the capacitance C in nF.

L = 100 µHf0 = 100 kHz
C = nF
3.Medium
V4.7 kΩ4.7 mH2.2 µF

A parallel RLC circuit has R = 4.7 kΩ, L = 4.7 mH and C = 2.2 µF. Find its quality factor Q.

R = 4.7 kΩL = 4.7 mHC = 2.2 µF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 22 mHC = 220 pF

In an ideal LC circuit with L = 22 mH and C = 220 pF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 22 mHC = 220 pF
t = µs
5.Hard
C = 4.7 nFr = 5 ΩL = 220 µH

A parallel tank circuit is made of a 4.7 nF capacitor and a 220 µH coil with a winding resistance of 5 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 220 µHC = 4.7 nFr = 5 Ω
RD = kΩ
6.Hard
f|I|0.7071f0​ = ?8 kHz9.6 kHzBW

The half-power frequencies of a resonance curve are 8 kHz and 9.6 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 8 kHzf2 = 9.6 kHz
Q =

Answer key

  1. 1. f0 = 494.9 kHz
  2. 2. C = 25.33 nF
  3. 3. Q = 101.7
  4. 4. t = 3.456 µs
  5. 5. RD = 9.362 kΩ
  6. 6. Q = 5.477

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