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 = 220 nF+−20 VL = 22 µHiL​

A 220 nF capacitor charged to 20 V is switched across an ideal 22 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 220 nFV0 = 20 VL = 22 µH
Imax = mA
2.Easy
C = 10 µFL = 22 µH

An ideal LC circuit has L = 22 µH and C = 10 µF. Find its natural (resonance) frequency f0 in kHz.

L = 22 µHC = 10 µF
f0 = kHz
3.Medium
C = 4.7 nF+−2.25 VL = 100 µHiL​

A 4.7 nF capacitor charged to 9 V oscillates with an ideal 100 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 2.25 V, in nJ.

C = 4.7 nFV0 = 9 VvC = 2.25 V
WL = nJ
4.Medium
f|I|0.7071100 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 100 kHz with Q = 2.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 100 kHzQ = 2.5
f1 = kHz
5.Hard
V1 Ω47 µH2.2 µF50 mA

A series RLC circuit (R = 1 Ω, L = 47 µH, C = 2.2 µF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 1 ΩL = 47 µHC = 2.2 µFIm = 50 mA
Ecycle = nJ
6.Hard
C = 22 nFr = 5 ΩL = 22 µH

A parallel tank circuit is made of a 22 nF capacitor and a 22 µH coil with a winding resistance of 5 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 22 µHC = 22 nFr = 5 Ω
RD = kΩ

Answer key

  1. 1. Imax = 2000 mA
  2. 2. f0 = 10.73 kHz
  3. 3. WL = 178.5 nJ
  4. 4. f1 = 81.98 kHz
  5. 5. Ecycle = 79.86 nJ
  6. 6. RD = 0.2 kΩ

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