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 = ?L = 100 mH

An LC circuit with L = 100 mH must resonate at 2 kHz. Find the capacitance C in nF.

L = 100 mHf0 = 2 kHz
C = nF
2.Easy
f|I|0.70711.6 MHzf1​f2​BW = 64 kHz

A resonance curve peaks at 1.6 MHz, and its half-power points are 64 kHz apart. Find the quality factor Q.

f0 = 1.6 MHzBW = 64 kHz
Q =
3.Medium
V2 Ω1 mH1 µF

A series RLC circuit has R = 2 Ω, L = 1 mH and C = 1 µF. Find its bandwidth BW in Hz.

R = 2 ΩL = 1 mHC = 1 µF
BW = Hz
4.Medium
tvC​iL​T/4 = ?T/2TL = 47 mHC = 470 pF

In an ideal LC circuit with L = 47 mH and C = 470 pF, 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 = 47 mHC = 470 pF
t = µs
5.Hard
C = 100 pFr = 20 ΩL = 4.7 mH

A parallel tank circuit is made of a 100 pF capacitor and a 4.7 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 = 4.7 mHC = 100 pFr = 20 Ω
RD = kΩ
6.Hard
f|I|0.7071f0​ = ?400 kHz420 kHzBW

The half-power frequencies of a resonance curve are 400 kHz and 420 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 400 kHzf2 = 420 kHz
Q =

Answer key

  1. 1. C = 63.33 nF
  2. 2. Q = 25
  3. 3. BW = 318.3 Hz
  4. 4. t = 7.383 µs
  5. 5. RD = 2350 kΩ
  6. 6. Q = 20.49

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