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 = 100 nF+−9 VL = 10 µHiL​

A 100 nF capacitor charged to 9 V is switched across an ideal 10 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 100 nFV0 = 9 VL = 10 µH
Imax = mA
2.Easy
f|I|0.7071100 kHzf1​f2​BW = 5 kHz

A resonance curve peaks at 100 kHz, and its half-power points are 5 kHz apart. Find the quality factor Q.

f0 = 100 kHzBW = 5 kHz
Q =
3.Medium
tvC​iL​T/4 = ?T/2TL = 0.47 µHC = 2.2 µF

In an ideal LC circuit with L = 0.47 µH and C = 2.2 µF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 0.47 µHC = 2.2 µF
t = µs
4.Medium
f|I|0.707120 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 20 kHz with Q = 4. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 20 kHzQ = 4
f1 = kHz
5.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 100 kHz and a bandwidth of 4 kHz. Find the capacitance C in nF.

R = 5 Ωf0 = 100 kHzBW = 4 kHz
C = nF
6.Hard
V5 Ω1 mH1 nF200 mA

A series RLC circuit (R = 5 Ω, L = 1 mH, C = 1 nF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 1 mHC = 1 nFIm = 200 mA
Ecycle = nJ

Answer key

  1. 1. Imax = 900 mA
  2. 2. Q = 20
  3. 3. t = 1.597 µs
  4. 4. f1 = 17.66 kHz
  5. 5. C = 12.73 nF
  6. 6. Ecycle = 628.3 nJ

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