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
f|I|0.707110 kHzf1​f2​BW = 400 Hz

A resonance curve peaks at 10 kHz, and its half-power points are 400 Hz apart. Find the quality factor Q.

f0 = 10 kHzBW = 400 Hz
Q =
2.Easy
C = 47 nF+−15 VL = 2.2 mHiL​

A 47 nF capacitor charged to 15 V is switched across an ideal 2.2 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 47 nFV0 = 15 VL = 2.2 mH
Imax = mA
3.Medium
V4.7 kΩ1 mH22 nF

A parallel RLC circuit has R = 4.7 kΩ, L = 1 mH and C = 22 nF. Find its quality factor Q.

R = 4.7 kΩL = 1 mHC = 22 nF
Q =
4.Medium
V1 Ω1 mH47 nF

A series RLC circuit has R = 1 Ω, L = 1 mH and C = 47 nF. Find its quality factor Q.

R = 1 ΩL = 1 mHC = 47 nF
Q =
5.Hard
C = 470 nFR = 0.5 ΩL = 220 µH

A charged 470 nF capacitor discharges through a 220 µH coil with a total series resistance of 0.5 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 = 220 µHC = 470 nFR = 0.5 Ω
n =
6.Hard
C = 22 nFr = 2 ΩL = 10 mH

A parallel tank circuit is made of a 22 nF capacitor and a 10 mH coil with a winding resistance of 2 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 10 mHC = 22 nFr = 2 Ω
RD = kΩ

Answer key

  1. 1. Q = 25
  2. 2. Imax = 69.33 mA
  3. 3. Q = 22.04
  4. 4. Q = 145.9
  5. 5. n = 9.547
  6. 6. RD = 227.3 kΩ

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