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 = 10 nFL = 1 µH

An ideal LC circuit has L = 1 µH and C = 10 nF. Find its natural (resonance) frequency f0 in MHz.

L = 1 µHC = 10 nF
f0 = MHz
2.Easy
tvC​iL​T/4T/2TV0​ = 5 VC = 4.7 nF

A 4.7 nF capacitor is charged to 5 V and then connected to an ideal 1 mH inductor. Find the total energy W that swings between them, in nJ.

C = 4.7 nFV0 = 5 VL = 1 mH
W = nJ
3.Medium
V47 Ω100 µH10 nF

A series RLC circuit has R = 47 Ω, L = 100 µH and C = 10 nF. Find its bandwidth BW in kHz.

R = 47 ΩL = 100 µHC = 10 nF
BW = kHz
4.Medium
V47 Ω100 µH470 pF

A series RLC circuit has R = 47 Ω, L = 100 µH and C = 470 pF. Find its quality factor Q.

R = 47 ΩL = 100 µHC = 470 pF
Q =
5.Hard
f|I|0.7071f0​ = ?20 kHz50 kHzBW

The half-power frequencies of a resonance curve are 20 kHz and 50 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 20 kHzf2 = 50 kHz
Q =
6.Hard
C = 470 nFr = 1 ΩL = 470 µH

A parallel tank circuit is made of a 470 nF capacitor and a 470 µH coil with a winding resistance of 1 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 470 µHC = 470 nFr = 1 Ω
RD = kΩ

Answer key

  1. 1. f0 = 1.592 MHz
  2. 2. W = 58.75 nJ
  3. 3. BW = 74.8 kHz
  4. 4. Q = 9.814
  5. 5. Q = 1.054
  6. 6. RD = 1 kΩ

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