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 = 4.7 mH

An LC circuit with L = 4.7 mH must resonate at 500 kHz. Find the capacitance C in nF.

L = 4.7 mHf0 = 500 kHz
C = nF
2.Easy
C = 100 pF+−24 VL = 470 µHiL​

A 100 pF capacitor charged to 24 V is switched across an ideal 470 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 100 pFV0 = 24 VL = 470 µH
Imax = mA
3.Medium
V4.7 kΩ470 µH10 nF

A parallel RLC circuit has R = 4.7 kΩ, L = 470 µH and C = 10 nF. Find its quality factor Q.

R = 4.7 kΩL = 470 µHC = 10 nF
Q =
4.Medium
V5 Ω220 µH220 nF

A series RLC circuit has R = 5 Ω, L = 220 µH and C = 220 nF. Find its quality factor Q.

R = 5 ΩL = 220 µHC = 220 nF
Q =
5.Hard
V1 Ω47 µH100 nF50 mA

A series RLC circuit (R = 1 Ω, L = 47 µH, C = 100 nF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 1 ΩL = 47 µHC = 100 nFIm = 50 mA
Ecycle = nJ
6.Hard
C = 220 pFR = 20 ΩL = 4.7 mH

A charged 220 pF capacitor discharges through a 4.7 mH coil with a total series resistance of 20 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 = 4.7 mHC = 220 pFR = 20 Ω
n =

Answer key

  1. 1. C = 0.02156 nF
  2. 2. Imax = 11.07 mA
  3. 3. Q = 21.68
  4. 4. Q = 6.325
  5. 5. Ecycle = 17.03 nJ
  6. 6. n = 50.99

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