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 = 470 nFL = 4.7 mH

An ideal LC circuit has L = 4.7 mH and C = 470 nF. Find its natural (resonance) frequency f0 in kHz.

L = 4.7 mHC = 470 nF
f0 = kHz
2.Easy
C = ?L = 10 mH

An LC circuit with L = 10 mH must resonate at 2 kHz. Find the capacitance C in nF.

L = 10 mHf0 = 2 kHz
C = nF
3.Medium
V10 Ω47 mH220 nF

A series RLC circuit has R = 10 Ω, L = 47 mH and C = 220 nF. Find its quality factor Q.

R = 10 ΩL = 47 mHC = 220 nF
Q =
4.Medium
C = 22 nF+−3.6 VL = 22 mHiL​

A 22 nF capacitor charged to 9 V oscillates with an ideal 22 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 3.6 V, in nJ.

C = 22 nFV0 = 9 VvC = 3.6 V
WL = nJ
5.Hard
C = 47 nFr = 10 ΩL = 4.7 mH

A parallel tank circuit is made of a 47 nF capacitor and a 4.7 mH coil with a winding resistance of 10 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 4.7 mHC = 47 nFr = 10 Ω
RD = kΩ
6.Hard
V10 Ω2.2 mH22 nF20 mA

A series RLC circuit (R = 10 Ω, L = 2.2 mH, 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 = 10 ΩL = 2.2 mHC = 22 nFIm = 20 mA
Ecycle = nJ

Answer key

  1. 1. f0 = 3.386 kHz
  2. 2. C = 633.3 nF
  3. 3. Q = 46.22
  4. 4. WL = 748.4 nJ
  5. 5. RD = 10 kΩ
  6. 6. Ecycle = 87.42 nJ

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