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
f|I|0.707110 kHzf1​f2​BW = ?

A tuned circuit resonates at 10 kHz and has a quality factor Q = 12. Find its bandwidth BW in Hz.

f0 = 10 kHzQ = 12
BW = Hz
2.Easy
C = 2.2 nF+−12 VL = 100 µHiL​

A 2.2 nF capacitor charged to 12 V is switched across an ideal 100 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 2.2 nFV0 = 12 VL = 100 µH
Imax = mA
3.Medium
V2 Ω470 µH2.2 µF

A series RLC circuit has R = 2 Ω, L = 470 µH and C = 2.2 µF. Find its quality factor Q.

R = 2 ΩL = 470 µHC = 2.2 µF
Q =
4.Medium
C = 1 nF+−4.8 VL = 220 µHiL​

A 1 nF capacitor charged to 6 V oscillates with an ideal 220 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 4.8 V, in nJ.

C = 1 nFV0 = 6 VvC = 4.8 V
WL = nJ
5.Hard
V10 Ω100 µH47 nF50 mA

A series RLC circuit (R = 10 Ω, L = 100 µH, C = 47 nF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 10 ΩL = 100 µHC = 47 nFIm = 50 mA
Ecycle = nJ
6.Hard
V50 ΩLC = ?

Design a series RLC filter with a total resistance of 50 Ω, a resonance frequency of 50 kHz and a bandwidth of 5 kHz. Find the capacitance C in nF.

R = 50 Ωf0 = 50 kHzBW = 5 kHz
C = nF

Answer key

  1. 1. BW = 833.3 Hz
  2. 2. Imax = 56.28 mA
  3. 3. Q = 7.308
  4. 4. WL = 6.48 nJ
  5. 5. Ecycle = 170.3 nJ
  6. 6. C = 6.366 nF

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