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|0.70711 kHzf1​f2​BW = 83.33 Hz

A resonance curve peaks at 1 kHz, and its half-power points are 83.33 Hz apart. Find the quality factor Q.

f0 = 1 kHzBW = 83.33 Hz
Q =
2.Easy
f|I|0.7071100 kHzf1​f2​BW = ?

A tuned circuit resonates at 100 kHz and has a quality factor Q = 8. Find its bandwidth BW in kHz.

f0 = 100 kHzQ = 8
BW = kHz
3.Medium
C = 10 nF+−1.2 VL = 47 mHiL​

A 10 nF capacitor charged to 6 V oscillates with an ideal 47 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 1.2 V, in nJ.

C = 10 nFV0 = 6 VvC = 1.2 V
WL = nJ
4.Medium
V22 Ω1 mH220 nF

A series RLC circuit has R = 22 Ω, L = 1 mH and C = 220 nF. Find its bandwidth BW in kHz.

R = 22 ΩL = 1 mHC = 220 nF
BW = kHz
5.Hard
f|I|0.7071f0​ = ?50 kHz125 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 125 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 125 kHz
Q =
6.Hard
V22 Ω47 mH22 nF500 mA

A series RLC circuit (R = 22 Ω, L = 47 mH, C = 22 nF) is driven at resonance with a current amplitude of 500 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 22 ΩL = 47 mHC = 22 nFIm = 500 mA
Ecycle = µJ

Answer key

  1. 1. Q = 12
  2. 2. BW = 12.5 kHz
  3. 3. WL = 172.8 nJ
  4. 4. BW = 3.501 kHz
  5. 5. Q = 1.054
  6. 6. Ecycle = 555.6 µJ

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