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|0.7071100 kHzf1​f2​BW = ?

A tuned circuit resonates at 100 kHz and has a quality factor Q = 20. Find its bandwidth BW in kHz.

f0 = 100 kHzQ = 20
BW = kHz
2.Easy
C = 22 nF+−12 VL = 0.47 µHiL​

A 22 nF capacitor charged to 12 V is switched across an ideal 0.47 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 22 nFV0 = 12 VL = 0.47 µH
Imax = mA
3.Medium
f|I|0.70711 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 1 kHz with Q = 5. Find the lower half-power frequency f1 exactly, in Hz.

f0 = 1 kHzQ = 5
f1 = Hz
4.Medium
tvC​iL​T/4 = ?T/2TL = 22 µHC = 10 µF

In an ideal LC circuit with L = 22 µH and C = 10 µF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 22 µHC = 10 µF
t = µs
5.Hard
f|I|0.7071f0​ = ?10 kHz20 kHzBW

The half-power frequencies of a resonance curve are 10 kHz and 20 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 10 kHzf2 = 20 kHz
Q =
6.Hard
C = 220 pFr = 10 ΩL = 4.7 mH

A parallel tank circuit is made of a 220 pF 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 = 220 pFr = 10 Ω
RD = kΩ

Answer key

  1. 1. BW = 5 kHz
  2. 2. Imax = 2596 mA
  3. 3. f1 = 905 Hz
  4. 4. t = 23.3 µs
  5. 5. Q = 1.414
  6. 6. RD = 2136 kΩ

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