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 pF+−12 VL = 22 mHiL​

A 220 pF capacitor charged to 12 V is switched across an ideal 22 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 220 pFV0 = 12 VL = 22 mH
Imax = mA
2.Easy
C = 4.7 nFL = 10 mH

An ideal LC circuit has L = 10 mH and C = 4.7 nF. Find its natural (resonance) frequency f0 in kHz.

L = 10 mHC = 4.7 nF
f0 = kHz
3.Medium
V47 Ω10 mH470 nF

A series RLC circuit has R = 47 Ω, L = 10 mH and C = 470 nF. Find its quality factor Q.

R = 47 ΩL = 10 mHC = 470 nF
Q =
4.Medium
V10 Ω4.7 mH100 nF

A series RLC circuit has R = 10 Ω, L = 4.7 mH and C = 100 nF. Find its quality factor Q.

R = 10 ΩL = 4.7 mHC = 100 nF
Q =
5.Hard
V22 Ω10 mH4.7 nF500 mA

A series RLC circuit (R = 22 Ω, L = 10 mH, C = 4.7 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 = 22 ΩL = 10 mHC = 4.7 nFIm = 500 mA
Ecycle = µJ
6.Hard
C = 220 nFr = 1 ΩL = 1 mH

A parallel tank circuit is made of a 220 nF capacitor and a 1 mH 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 = 1 mHC = 220 nFr = 1 Ω
RD = kΩ

Answer key

  1. 1. Imax = 1.2 mA
  2. 2. f0 = 23.22 kHz
  3. 3. Q = 3.104
  4. 4. Q = 21.68
  5. 5. Ecycle = 118.5 µJ
  6. 6. RD = 4.545 kΩ

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