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|0.707150 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 =
2.Easy
f|I|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 80. Find its bandwidth BW in kHz.

f0 = 10.7 MHzQ = 80
BW = kHz
3.Medium
V47 kΩ2.2 mH1 nF

A parallel RLC circuit has R = 47 kΩ, L = 2.2 mH and C = 1 nF. Find its quality factor Q.

R = 47 kΩL = 2.2 mHC = 1 nF
Q =
4.Medium
V4.7 kΩ100 mH22 nF

A parallel RLC circuit has R = 4.7 kΩ, L = 100 mH and C = 22 nF. Find its quality factor Q.

R = 4.7 kΩL = 100 mHC = 22 nF
Q =
5.Hard
V22 Ω1 mH220 pF200 mA

A series RLC circuit (R = 22 Ω, L = 1 mH, C = 220 pF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 22 ΩL = 1 mHC = 220 pFIm = 200 mA
Ecycle = µJ
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 = 25
  2. 2. BW = 133.8 kHz
  3. 3. Q = 31.69
  4. 4. Q = 2.204
  5. 5. Ecycle = 1.297 µJ
  6. 6. C = 31.83 nF

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