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
C = 2.2 µFL = 10 µH

An ideal LC circuit has L = 10 µH and C = 2.2 µF. Find its natural (resonance) frequency f0 in kHz.

L = 10 µHC = 2.2 µF
f0 = kHz
2.Easy
C = 10 nF+−6 VL = 47 µHiL​

A 10 nF capacitor charged to 6 V is switched across an ideal 47 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 10 nFV0 = 6 VL = 47 µH
Imax = mA
3.Medium
V22 Ω470 µH220 nF

A series RLC circuit has R = 22 Ω, L = 470 µH and C = 220 nF. Find its quality factor Q.

R = 22 ΩL = 470 µHC = 220 nF
Q =
4.Medium
V1 Ω2.2 mH1 µF

A series RLC circuit has R = 1 Ω, L = 2.2 mH and C = 1 µF. Find its bandwidth BW in Hz.

R = 1 ΩL = 2.2 mHC = 1 µF
BW = Hz
5.Hard
C = 220 nFr = 0.5 ΩL = 220 µH

A parallel tank circuit is made of a 220 nF capacitor and a 220 µH coil with a winding resistance of 0.5 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 220 µHC = 220 nFr = 0.5 Ω
RD = kΩ
6.Hard
f|I|0.7071f0​ = ?2 kHz3 kHzBW

The half-power frequencies of a resonance curve are 2 kHz and 3 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 2 kHzf2 = 3 kHz
Q =

Answer key

  1. 1. f0 = 33.93 kHz
  2. 2. Imax = 87.52 mA
  3. 3. Q = 2.101
  4. 4. BW = 72.34 Hz
  5. 5. RD = 2 kΩ
  6. 6. Q = 2.449

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