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​ = 9 VC = 2.2 nF

A 2.2 nF capacitor is charged to 9 V and then connected to an ideal 22 mH inductor. Find the total energy W that swings between them, in nJ.

C = 2.2 nFV0 = 9 VL = 22 mH
W = nJ
2.Easy
C = ?L = 0.1 µH

An LC circuit with L = 0.1 µH must resonate at 1 MHz. Find the capacitance C in nF.

L = 0.1 µHf0 = 1 MHz
C = nF
3.Medium
V2.2 kΩ22 µH220 nF

A parallel RLC circuit has R = 2.2 kΩ, L = 22 µH and C = 220 nF. Find its quality factor Q.

R = 2.2 kΩL = 22 µHC = 220 nF
Q =
4.Medium
V47 Ω4.7 mH100 pF

A series RLC circuit has R = 47 Ω, L = 4.7 mH and C = 100 pF. Find its bandwidth BW in kHz.

R = 47 ΩL = 4.7 mHC = 100 pF
BW = kHz
5.Hard
V10 Ω4.7 mH220 nF50 mA

A series RLC circuit (R = 10 Ω, L = 4.7 mH, C = 220 nF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 10 ΩL = 4.7 mHC = 220 nFIm = 50 mA
Ecycle = µJ
6.Hard
C = 4.7 nFR = 0.5 ΩL = 47 µH

A charged 4.7 nF capacitor discharges through a 47 µH coil with a total series resistance of 0.5 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 = 47 µHC = 4.7 nFR = 0.5 Ω
n =

Answer key

  1. 1. W = 89.1 nJ
  2. 2. C = 253.3 nF
  3. 3. Q = 220
  4. 4. BW = 1.592 kHz
  5. 5. Ecycle = 2.526 µJ
  6. 6. n = 44.13

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