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 = 1 µF+−9 VL = 470 µHiL​

A 1 µF capacitor charged to 9 V is switched across an ideal 470 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 1 µFV0 = 9 VL = 470 µH
Imax = mA
2.Easy
C = ?L = 4.7 mH

An LC circuit with L = 4.7 mH must resonate at 200 kHz. Find the capacitance C in nF.

L = 4.7 mHf0 = 200 kHz
C = nF
3.Medium
tvC​iL​T/4 = ?T/2TL = 10 µHC = 220 nF

In an ideal LC circuit with L = 10 µH and C = 220 nF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 10 µHC = 220 nF
t = µs
4.Medium
tvC​iL​T/4 = ?T/2TL = 1 mHC = 100 pF

In an ideal LC circuit with L = 1 mH and C = 100 pF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 1 mHC = 100 pF
t = µs
5.Hard
C = 1 nFr = 1 ΩL = 22 µH

A parallel tank circuit is made of a 1 nF capacitor and a 22 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 = 22 µHC = 1 nFr = 1 Ω
RD = kΩ
6.Hard
V22 Ω100 µH22 nF20 mA

A series RLC circuit (R = 22 Ω, L = 100 µH, C = 22 nF) is driven at resonance with a current amplitude of 20 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 22 ΩL = 100 µHC = 22 nFIm = 20 mA
Ecycle = nJ

Answer key

  1. 1. Imax = 415.1 mA
  2. 2. C = 0.1347 nF
  3. 3. t = 2.33 µs
  4. 4. t = 0.4967 µs
  5. 5. RD = 22 kΩ
  6. 6. Ecycle = 41.01 nJ

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