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
f|I|0.70715 kHzf1​f2​BW = 200 Hz

A resonance curve peaks at 5 kHz, and its half-power points are 200 Hz apart. Find the quality factor Q.

f0 = 5 kHzBW = 200 Hz
Q =
2.Easy
C = 2.2 nF+−9 VL = 47 µHiL​

A 2.2 nF capacitor charged to 9 V is switched across an ideal 47 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 2.2 nFV0 = 9 VL = 47 µH
Imax = mA
3.Medium
V2 Ω2.2 mH1 µF

A series RLC circuit has R = 2 Ω, L = 2.2 mH and C = 1 µF. Find its bandwidth BW in Hz.

R = 2 ΩL = 2.2 mHC = 1 µF
BW = Hz
4.Medium
V10 Ω2.2 mH470 nF

A series RLC circuit has R = 10 Ω, L = 2.2 mH and C = 470 nF. Find its bandwidth BW in Hz.

R = 10 ΩL = 2.2 mHC = 470 nF
BW = Hz
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 50 kHz and a bandwidth of 2 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 50 kHzBW = 2 kHz
C = nF
6.Hard
V5 Ω22 µH10 nF50 mA

A series RLC circuit (R = 5 Ω, L = 22 µH, C = 10 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 = 5 ΩL = 22 µHC = 10 nFIm = 50 mA
Ecycle = nJ

Answer key

  1. 1. Q = 25
  2. 2. Imax = 61.58 mA
  3. 3. BW = 144.7 Hz
  4. 4. BW = 723.4 Hz
  5. 5. C = 6.366 nF
  6. 6. Ecycle = 18.42 nJ

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