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|0.707110.7 MHzf1​f2​BW = 428 kHz

A resonance curve peaks at 10.7 MHz, and its half-power points are 428 kHz apart. Find the quality factor Q.

f0 = 10.7 MHzBW = 428 kHz
Q =
2.Easy
C = ?L = 1 mH

An LC circuit with L = 1 mH must resonate at 20 kHz. Find the capacitance C in nF.

L = 1 mHf0 = 20 kHz
C = nF
3.Medium
tvC​iL​T/4 = ?T/2TL = 1 µHC = 1 µF

In an ideal LC circuit with L = 1 µH and C = 1 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 = 1 µHC = 1 µF
t = µs
4.Medium
V10 Ω22 µH22 nF

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

R = 10 ΩL = 22 µHC = 22 nF
Q =
5.Hard
V22 Ω10 mH100 nF20 mA

A series RLC circuit (R = 22 Ω, L = 10 mH, C = 100 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 = 22 ΩL = 10 mHC = 100 nFIm = 20 mA
Ecycle = nJ
6.Hard
V2 Ω22 µH22 nF10 mA

A series RLC circuit (R = 2 Ω, L = 22 µH, C = 22 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 22 µHC = 22 nFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. Q = 25
  2. 2. C = 63.33 nF
  3. 3. t = 1.571 µs
  4. 4. Q = 3.162
  5. 5. Ecycle = 874.2 nJ
  6. 6. Ecycle = 0.4371 nJ

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