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 = 1 µF+−20 VL = 47 µHiL​

A 1 µF capacitor charged to 20 V is switched across an ideal 47 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 1 µFV0 = 20 VL = 47 µH
Imax = mA
2.Easy
C = 4.7 nFL = 100 mH

An ideal LC circuit has L = 100 mH and C = 4.7 nF. Find its natural (resonance) frequency f0 in kHz.

L = 100 mHC = 4.7 nF
f0 = kHz
3.Medium
V2.2 kΩ1 mH2.2 µF

A parallel RLC circuit has R = 2.2 kΩ, L = 1 mH and C = 2.2 µF. Find its quality factor Q.

R = 2.2 kΩL = 1 mHC = 2.2 µF
Q =
4.Medium
C = 220 nF+−2 VL = 47 mHiL​

A 220 nF capacitor charged to 10 V oscillates with an ideal 47 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 2 V, in µJ.

C = 220 nFV0 = 10 VvC = 2 V
WL = µJ
5.Hard
f|I|0.7071f0​ = ?1 kHz1.1 kHzBW

The half-power frequencies of a resonance curve are 1 kHz and 1.1 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 1 kHzf2 = 1.1 kHz
Q =
6.Hard
V1 Ω10 µH47 nF50 mA

A series RLC circuit (R = 1 Ω, L = 10 µH, C = 47 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 = 10 µHC = 47 nFIm = 50 mA
Ecycle = nJ

Answer key

  1. 1. Imax = 2917 mA
  2. 2. f0 = 7.341 kHz
  3. 3. Q = 103.2
  4. 4. WL = 10.56 µJ
  5. 5. Q = 10.49
  6. 6. Ecycle = 5.384 nJ

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