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 pFL = 100 mH

An ideal LC circuit has L = 100 mH and C = 100 pF. Find its natural (resonance) frequency f0 in kHz.

L = 100 mHC = 100 pF
f0 = kHz
2.Easy
f|I|0.70712 kHzf1​f2​BW = 80 Hz

A resonance curve peaks at 2 kHz, and its half-power points are 80 Hz apart. Find the quality factor Q.

f0 = 2 kHzBW = 80 Hz
Q =
3.Medium
tvC​iL​T/4 = ?T/2TL = 2.2 mHC = 470 pF

In an ideal LC circuit with L = 2.2 mH and C = 470 pF, 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 = 2.2 mHC = 470 pF
t = µs
4.Medium
V2 Ω47 µH470 nF

A series RLC circuit has R = 2 Ω, L = 47 µH and C = 470 nF. Find its bandwidth BW in kHz.

R = 2 ΩL = 47 µHC = 470 nF
BW = kHz
5.Hard
V2 Ω100 µH10 nF50 mA

A series RLC circuit (R = 2 Ω, L = 100 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 = 2 ΩL = 100 µHC = 10 nFIm = 50 mA
Ecycle = nJ
6.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 200 kHz and a bandwidth of 4 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 200 kHzBW = 4 kHz
C = nF

Answer key

  1. 1. f0 = 50.33 kHz
  2. 2. Q = 25
  3. 3. t = 1.597 µs
  4. 4. BW = 6.773 kHz
  5. 5. Ecycle = 15.71 nJ
  6. 6. C = 0.7958 nF

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