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 = 47 nF+−6 VL = 2.2 mHiL​

A 47 nF capacitor charged to 6 V is switched across an ideal 2.2 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 47 nFV0 = 6 VL = 2.2 mH
Imax = mA
2.Easy
C = 1 nFL = 47 µH

An ideal LC circuit has L = 47 µH and C = 1 nF. Find its natural (resonance) frequency f0 in kHz.

L = 47 µHC = 1 nF
f0 = kHz
3.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 =
4.Medium
f|I|0.70712 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 2 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 2 kHzQ = 1.5
f1 = kHz
5.Hard
VR = ?4.7 mHC

A series resonant circuit uses a 4.7 mH inductor. Which total series resistance R gives a bandwidth of 1 kHz?

L = 4.7 mHBW = 1 kHz
R = Ω
6.Hard
C = 47 nFR = 5 ΩL = 47 mH

A charged 47 nF capacitor discharges through a 47 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 = 47 mHC = 47 nFR = 5 Ω
n =

Answer key

  1. 1. Imax = 27.73 mA
  2. 2. f0 = 734.1 kHz
  3. 3. Q = 6.325
  4. 4. f1 = 1.442 kHz
  5. 5. R = 29.53 Ω
  6. 6. n = 44.13

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