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|0.7071455 kHzf1​f2​BW = ?

A tuned circuit resonates at 455 kHz and has a quality factor Q = 8. Find its bandwidth BW in kHz.

f0 = 455 kHzQ = 8
BW = kHz
2.Easy
f|I|0.707150 kHzf1​f2​BW = 2 kHz

A resonance curve peaks at 50 kHz, and its half-power points are 2 kHz apart. Find the quality factor Q.

f0 = 50 kHzBW = 2 kHz
Q =
3.Medium
tvC​iL​T/4 = ?T/2TL = 4.7 mHC = 100 pF

In an ideal LC circuit with L = 4.7 mH and C = 100 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 = 4.7 mHC = 100 pF
t = µs
4.Medium
V10 kΩ1 mH10 nF

A parallel RLC circuit has R = 10 kΩ, L = 1 mH and C = 10 nF. Find its quality factor Q.

R = 10 kΩL = 1 mHC = 10 nF
Q =
5.Hard
V10 ΩLC = ?

Design a series RLC filter with a total resistance of 10 Ω, a resonance frequency of 200 kHz and a bandwidth of 5 kHz. Find the capacitance C in nF.

R = 10 Ωf0 = 200 kHzBW = 5 kHz
C = nF
6.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 200 kHz and a bandwidth of 20 kHz. Find the capacitance C in nF.

R = 100 Ωf0 = 200 kHzBW = 20 kHz
C = nF

Answer key

  1. 1. BW = 56.88 kHz
  2. 2. Q = 25
  3. 3. t = 1.077 µs
  4. 4. Q = 31.62
  5. 5. C = 1.989 nF
  6. 6. C = 0.7958 nF

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