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|0.70711 MHzf1​f2​BW = 100 kHz

A resonance curve peaks at 1 MHz, and its half-power points are 100 kHz apart. Find the quality factor Q.

f0 = 1 MHzBW = 100 kHz
Q =
2.Easy
C = 4.7 nF+−10 VL = 4.7 mHiL​

A 4.7 nF capacitor charged to 10 V is switched across an ideal 4.7 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 4.7 nFV0 = 10 VL = 4.7 mH
Imax = mA
3.Medium
V100 Ω2.2 mH22 nF

A series RLC circuit has R = 100 Ω, L = 2.2 mH and C = 22 nF. Find its quality factor Q.

R = 100 ΩL = 2.2 mHC = 22 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 220 µHC = 1 nF

In an ideal LC circuit with L = 220 µH and C = 1 nF, 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 = 220 µHC = 1 nF
t = µs
5.Hard
V22 Ω100 mH100 nF100 mA

A series RLC circuit (R = 22 Ω, L = 100 mH, C = 100 nF) is driven at resonance with a current amplitude of 100 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 22 ΩL = 100 mHC = 100 nFIm = 100 mA
Ecycle = µJ
6.Hard
V5 Ω1 mH470 nF20 mA

A series RLC circuit (R = 5 Ω, L = 1 mH, C = 470 nF) is driven at resonance with a current amplitude of 20 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 1 mHC = 470 nFIm = 20 mA
Ecycle = nJ

Answer key

  1. 1. Q = 10
  2. 2. Imax = 10 mA
  3. 3. Q = 3.162
  4. 4. t = 0.7368 µs
  5. 5. Ecycle = 69.12 µJ
  6. 6. Ecycle = 136.2 nJ

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