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|0.70712 kHzf1​f2​BW = 166.7 Hz

A resonance curve peaks at 2 kHz, and its half-power points are 166.7 Hz apart. Find the quality factor Q.

f0 = 2 kHzBW = 166.7 Hz
Q =
2.Easy
tvC​iL​T/4T/2TV0​ = 9 VC = 470 pF

A 470 pF capacitor is charged to 9 V and then connected to an ideal 47 mH inductor. Find the total energy W that swings between them, in nJ.

C = 470 pFV0 = 9 VL = 47 mH
W = nJ
3.Medium
V47 Ω4.7 mH220 pF

A series RLC circuit has R = 47 Ω, L = 4.7 mH and C = 220 pF. Find its bandwidth BW in kHz.

R = 47 ΩL = 4.7 mHC = 220 pF
BW = kHz
4.Medium
V10 Ω1 mH220 nF

A series RLC circuit has R = 10 Ω, L = 1 mH and C = 220 nF. Find its quality factor Q.

R = 10 ΩL = 1 mHC = 220 nF
Q =
5.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 100 kHz and a bandwidth of 5 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 100 kHzBW = 5 kHz
C = nF
6.Hard
V2 Ω4.7 mH1 µF200 mA

A series RLC circuit (R = 2 Ω, L = 4.7 mH, C = 1 µF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 2 ΩL = 4.7 mHC = 1 µFIm = 200 mA
Ecycle = µJ

Answer key

  1. 1. Q = 12
  2. 2. W = 19.04 nJ
  3. 3. BW = 1.592 kHz
  4. 4. Q = 6.742
  5. 5. C = 3.979 nF
  6. 6. Ecycle = 17.23 µJ

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