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 = 9.1 kHz

A resonance curve peaks at 455 kHz, and its half-power points are 9.1 kHz apart. Find the quality factor Q.

f0 = 455 kHzBW = 9.1 kHz
Q =
2.Easy
C = 22 nF+−5 VL = 1 µHiL​

A 22 nF capacitor charged to 5 V is switched across an ideal 1 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 22 nFV0 = 5 VL = 1 µH
Imax = mA
3.Medium
V4.7 kΩ47 mH220 nF

A parallel RLC circuit has R = 4.7 kΩ, L = 47 mH and C = 220 nF. Find its quality factor Q.

R = 4.7 kΩL = 47 mHC = 220 nF
Q =
4.Medium
C = 470 nF+−12 VL = 470 µHiL​

A 470 nF capacitor charged to 15 V oscillates with an ideal 470 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 12 V, in µJ.

C = 470 nFV0 = 15 VvC = 12 V
WL = µJ
5.Hard
f|I|0.7071f0​ = ?8 kHz8.8 kHzBW

The half-power frequencies of a resonance curve are 8 kHz and 8.8 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 8 kHzf2 = 8.8 kHz
Q =
6.Hard
V22 Ω470 µH220 pF100 mA

A series RLC circuit (R = 22 Ω, L = 470 µH, C = 220 pF) is driven at resonance with a current amplitude of 100 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 22 ΩL = 470 µHC = 220 pFIm = 100 mA
Ecycle = nJ

Answer key

  1. 1. Q = 50
  2. 2. Imax = 741.6 mA
  3. 3. Q = 10.17
  4. 4. WL = 19.04 µJ
  5. 5. Q = 10.49
  6. 6. Ecycle = 222.2 nJ

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