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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
C = 47 nF+−10 VL = 100 µHiL​

A 47 nF capacitor charged to 10 V is switched across an ideal 100 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 47 nFV0 = 10 VL = 100 µH
Imax = mA
2.Easy
C = 1 µF+−50 VL = 470 µHiL​

A 1 µF capacitor charged to 50 V is switched across an ideal 470 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 1 µFV0 = 50 VL = 470 µH
Imax = mA
3.Medium
V220 Ω47 mH2.2 nF

A series RLC circuit has R = 220 Ω, L = 47 mH and C = 2.2 nF. Find its quality factor Q.

R = 220 ΩL = 47 mHC = 2.2 nF
Q =
4.Medium
V22 kΩ220 µH220 pF

A parallel RLC circuit has R = 22 kΩ, L = 220 µH and C = 220 pF. Find its quality factor Q.

R = 22 kΩL = 220 µHC = 220 pF
Q =
5.Hard
C = 100 nFR = 10 ΩL = 47 mH

A charged 100 nF capacitor discharges through a 47 mH coil with a total series resistance of 10 Ω, so the oscillation slowly dies out. Its amplitude decays as e−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 47 mHC = 100 nFR = 10 Ω
n =
6.Hard
C = 220 pFr = 20 ΩL = 10 mH

A parallel tank circuit is made of a 220 pF capacitor and a 10 mH coil with a winding resistance of 20 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 10 mHC = 220 pFr = 20 Ω
RD = kΩ

Answer key

  1. 1. Imax = 216.8 mA
  2. 2. Imax = 2306 mA
  3. 3. Q = 21.01
  4. 4. Q = 22
  5. 5. n = 15.13
  6. 6. RD = 2273 kΩ

Full step-by-step solutions: practise this topic on examproblems.com.