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
tvC​iL​T/4T/2TV0​ = 6 VC = 100 pF

A 100 pF capacitor is charged to 6 V and then connected to an ideal 4.7 mH inductor. Find the total energy W that swings between them, in nJ.

C = 100 pFV0 = 6 VL = 4.7 mH
W = nJ
2.Easy
f|I|0.70711 kHzf1​f2​BW = ?

A tuned circuit resonates at 1 kHz and has a quality factor Q = 20. Find its bandwidth BW in Hz.

f0 = 1 kHzQ = 20
BW = Hz
3.Medium
V100 kΩ22 mH22 nF

A parallel RLC circuit has R = 100 kΩ, L = 22 mH and C = 22 nF. Find its quality factor Q.

R = 100 kΩL = 22 mHC = 22 nF
Q =
4.Medium
V2 Ω10 mH1 µF

A series RLC circuit has R = 2 Ω, L = 10 mH and C = 1 µF. Find its quality factor Q.

R = 2 ΩL = 10 mHC = 1 µF
Q =
5.Hard
V1 Ω1 mH10 µF500 mA

A series RLC circuit (R = 1 Ω, L = 1 mH, C = 10 µF) is driven at resonance with a current amplitude of 500 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 1 ΩL = 1 mHC = 10 µFIm = 500 mA
Ecycle = µJ
6.Hard
C = 10 nFr = 0.5 ΩL = 2.2 mH

A parallel tank circuit is made of a 10 nF capacitor and a 2.2 mH 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 = 2.2 mHC = 10 nFr = 0.5 Ω
RD = kΩ

Answer key

  1. 1. W = 1.8 nJ
  2. 2. BW = 50 Hz
  3. 3. Q = 100
  4. 4. Q = 50
  5. 5. Ecycle = 78.54 µJ
  6. 6. RD = 440 kΩ

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