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 kHzf1​f2​BW = 2 kHz

A resonance curve peaks at 10 kHz, and its half-power points are 2 kHz apart. Find the quality factor Q.

f0 = 10 kHzBW = 2 kHz
Q =
2.Easy
f|I|0.7071100 kHzf1​f2​BW = 4 kHz

A resonance curve peaks at 100 kHz, and its half-power points are 4 kHz apart. Find the quality factor Q.

f0 = 100 kHzBW = 4 kHz
Q =
3.Medium
V10 Ω4.7 mH47 nF

A series RLC circuit has R = 10 Ω, L = 4.7 mH and C = 47 nF. Find its bandwidth BW in Hz.

R = 10 ΩL = 4.7 mHC = 47 nF
BW = Hz
4.Medium
V5 Ω100 µH47 nF

A series RLC circuit has R = 5 Ω, L = 100 µH and C = 47 nF. Find its quality factor Q.

R = 5 ΩL = 100 µHC = 47 nF
Q =
5.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 200 kHz and a bandwidth of 10 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 200 kHzBW = 10 kHz
C = nF
6.Hard
V5 ΩLC = ?

Design a series RLC filter with a total resistance of 5 Ω, a resonance frequency of 50 kHz and a bandwidth of 2.5 kHz. Find the capacitance C in nF.

R = 5 Ωf0 = 50 kHzBW = 2.5 kHz
C = nF

Answer key

  1. 1. Q = 5
  2. 2. Q = 25
  3. 3. BW = 338.6 Hz
  4. 4. Q = 9.225
  5. 5. C = 0.7958 nF
  6. 6. C = 31.83 nF

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