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 = ?L = 10 µH

An LC circuit with L = 10 µH must resonate at 455 kHz. Find the capacitance C in nF.

L = 10 µHf0 = 455 kHz
C = nF
2.Easy
C = ?L = 2.2 mH

An LC circuit with L = 2.2 mH must resonate at 5 kHz. Find the capacitance C in nF.

L = 2.2 mHf0 = 5 kHz
C = nF
3.Medium
V10 Ω4.7 mH470 nF

A series RLC circuit has R = 10 Ω, L = 4.7 mH and C = 470 nF. Find its bandwidth BW in Hz.

R = 10 ΩL = 4.7 mHC = 470 nF
BW = Hz
4.Medium
V1 Ω22 µH47 nF

A series RLC circuit has R = 1 Ω, L = 22 µH and C = 47 nF. Find its quality factor Q.

R = 1 ΩL = 22 µHC = 47 nF
Q =
5.Hard
C = 220 nFR = 5 ΩL = 100 mH

A charged 220 nF capacitor discharges through a 100 mH coil with a total series resistance of 5 Ω, so the oscillation slowly dies out. Its amplitude decays as e−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 100 mHC = 220 nFR = 5 Ω
n =
6.Hard
C = 4.7 nFr = 2 ΩL = 47 µH

A parallel tank circuit is made of a 4.7 nF capacitor and a 47 µH coil with a winding resistance of 2 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 47 µHC = 4.7 nFr = 2 Ω
RD = kΩ

Answer key

  1. 1. C = 12.24 nF
  2. 2. C = 460.6 nF
  3. 3. BW = 338.6 Hz
  4. 4. Q = 21.64
  5. 5. n = 29.75
  6. 6. RD = 5 kΩ

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