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 = 2.2 µF+−20 VL = 4.7 mHiL​

A 2.2 µF capacitor charged to 20 V is switched across an ideal 4.7 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 2.2 µFV0 = 20 VL = 4.7 mH
Imax = mA
2.Easy
f|I|0.70711 kHzf1​f2​BW = 20 Hz

A resonance curve peaks at 1 kHz, and its half-power points are 20 Hz apart. Find the quality factor Q.

f0 = 1 kHzBW = 20 Hz
Q =
3.Medium
V5 Ω10 µH22 nF

A series RLC circuit has R = 5 Ω, L = 10 µH and C = 22 nF. Find its quality factor Q.

R = 5 ΩL = 10 µHC = 22 nF
Q =
4.Medium
V5 Ω22 µH100 nF

A series RLC circuit has R = 5 Ω, L = 22 µH and C = 100 nF. Find its quality factor Q.

R = 5 ΩL = 22 µHC = 100 nF
Q =
5.Hard
V5 Ω22 mH1 µF200 mA

A series RLC circuit (R = 5 Ω, L = 22 mH, C = 1 µF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 5 ΩL = 22 mHC = 1 µFIm = 200 mA
Ecycle = µJ
6.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 20 kHz and a bandwidth of 500 Hz. Find the capacitance C in nF.

R = 5 Ωf0 = 20 kHzBW = 500 Hz
C = nF

Answer key

  1. 1. Imax = 432.7 mA
  2. 2. Q = 50
  3. 3. Q = 4.264
  4. 4. Q = 2.966
  5. 5. Ecycle = 93.19 µJ
  6. 6. C = 39.79 nF

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