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 = 220 nFL = 2.2 µH

An ideal LC circuit has L = 2.2 µH and C = 220 nF. Find its natural (resonance) frequency f0 in kHz.

L = 2.2 µHC = 220 nF
f0 = kHz
2.Easy
C = ?L = 100 µH

An LC circuit with L = 100 µH must resonate at 455 kHz. Find the capacitance C in nF.

L = 100 µHf0 = 455 kHz
C = nF
3.Medium
V10 kΩ1 mH470 nF

A parallel RLC circuit has R = 10 kΩ, L = 1 mH and C = 470 nF. Find its quality factor Q.

R = 10 kΩL = 1 mHC = 470 nF
Q =
4.Medium
V10 Ω10 mH1 µF

A series RLC circuit has R = 10 Ω, L = 10 mH and C = 1 µF. Find its bandwidth BW in Hz.

R = 10 ΩL = 10 mHC = 1 µF
BW = Hz
5.Hard
C = 470 pFr = 2 ΩL = 22 µH

A parallel tank circuit is made of a 470 pF capacitor and a 22 µH 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 = 22 µHC = 470 pFr = 2 Ω
RD = kΩ
6.Hard
V20 ΩLC = ?

Design a series RLC filter with a total resistance of 20 Ω, a resonance frequency of 455 kHz and a bandwidth of 18.2 kHz. Find the capacitance C in nF.

R = 20 Ωf0 = 455 kHzBW = 18.2 kHz
C = nF

Answer key

  1. 1. f0 = 228.8 kHz
  2. 2. C = 1.224 nF
  3. 3. Q = 216.8
  4. 4. BW = 159.2 Hz
  5. 5. RD = 23.4 kΩ
  6. 6. C = 0.6996 nF

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