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|0.70711 MHzf1​f2​BW = ?

A tuned circuit resonates at 1 MHz and has a quality factor Q = 10. Find its bandwidth BW in kHz.

f0 = 1 MHzQ = 10
BW = kHz
2.Easy
C = 47 nF+−6 VL = 22 mHiL​

A 47 nF capacitor charged to 6 V is switched across an ideal 22 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 47 nFV0 = 6 VL = 22 mH
Imax = mA
3.Medium
V2 Ω220 µH220 nF

A series RLC circuit has R = 2 Ω, L = 220 µH and C = 220 nF. Find its quality factor Q.

R = 2 ΩL = 220 µHC = 220 nF
Q =
4.Medium
V220 Ω10 mH22 nF

A series RLC circuit has R = 220 Ω, L = 10 mH and C = 22 nF. Find its quality factor Q.

R = 220 ΩL = 10 mHC = 22 nF
Q =
5.Hard
V22 Ω22 mH47 nF20 mA

A series RLC circuit (R = 22 Ω, L = 22 mH, C = 47 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 = 22 mHC = 47 nFIm = 20 mA
Ecycle = nJ
6.Hard
V10 ΩLC = ?

Design a series RLC filter with a total resistance of 10 Ω, a resonance frequency of 10 kHz and a bandwidth of 200 Hz. Find the capacitance C in nF.

R = 10 Ωf0 = 10 kHzBW = 200 Hz
C = nF

Answer key

  1. 1. BW = 100 kHz
  2. 2. Imax = 8.77 mA
  3. 3. Q = 15.81
  4. 4. Q = 3.065
  5. 5. Ecycle = 889 nJ
  6. 6. C = 31.83 nF

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