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 = 47 nF+−10 VL = 2.2 µHiL​

A 47 nF capacitor charged to 10 V is switched across an ideal 2.2 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 47 nFV0 = 10 VL = 2.2 µH
Imax = mA
2.Easy
C = ?L = 220 µH

An LC circuit with L = 220 µH must resonate at 200 kHz. Find the capacitance C in nF.

L = 220 µHf0 = 200 kHz
C = nF
3.Medium
tvC​iL​T/4 = ?T/2TL = 10 mHC = 1 nF

In an ideal LC circuit with L = 10 mH and C = 1 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 mHC = 1 nF
t = µs
4.Medium
f|I|0.707150 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 50 kHz with Q = 2.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 50 kHzQ = 2.5
f1 = kHz
5.Hard
C = 4.7 nFr = 2 ΩL = 10 mH

A parallel tank circuit is made of a 4.7 nF capacitor and a 10 mH coil with a winding resistance of 2 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 10 mHC = 4.7 nFr = 2 Ω
RD = kΩ
6.Hard
V1 Ω220 µH470 nF500 mA

A series RLC circuit (R = 1 Ω, L = 220 µH, C = 470 nF) 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 = 220 µHC = 470 nFIm = 500 mA
Ecycle = µJ

Answer key

  1. 1. Imax = 1462 mA
  2. 2. C = 2.878 nF
  3. 3. t = 4.967 µs
  4. 4. f1 = 40.99 kHz
  5. 5. RD = 1064 kΩ
  6. 6. Ecycle = 7.986 µJ

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