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 = 100 nF+−10 VL = 22 µHiL​

A 100 nF capacitor charged to 10 V is switched across an ideal 22 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 100 nFV0 = 10 VL = 22 µH
Imax = mA
2.Easy
f|I|0.7071100 kHzf1​f2​BW = ?

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

f0 = 100 kHzQ = 100
BW = kHz
3.Medium
V5 Ω10 mH470 nF

A series RLC circuit has R = 5 Ω, L = 10 mH and C = 470 nF. Find its quality factor Q.

R = 5 ΩL = 10 mHC = 470 nF
Q =
4.Medium
C = 10 µF+−4.8 VL = 1 mHiL​

A 10 µF capacitor charged to 24 V oscillates with an ideal 1 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 4.8 V, in mJ.

C = 10 µFV0 = 24 VvC = 4.8 V
WL = mJ
5.Hard
C = 22 nFr = 1 ΩL = 22 mH

A parallel tank circuit is made of a 22 nF capacitor and a 22 mH 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 = 22 mHC = 22 nFr = 1 Ω
RD = kΩ
6.Hard
f|I|0.7071f0​ = ?400 kHz420 kHzBW

The half-power frequencies of a resonance curve are 400 kHz and 420 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 400 kHzf2 = 420 kHz
Q =

Answer key

  1. 1. Imax = 674.2 mA
  2. 2. BW = 1 kHz
  3. 3. Q = 29.17
  4. 4. WL = 2.765 mJ
  5. 5. RD = 1000 kΩ
  6. 6. Q = 20.49

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