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
tvC​iL​T/4T/2TV0​ = 20 VC = 470 pF

A 470 pF capacitor is charged to 20 V and then connected to an ideal 100 µH inductor. Find the total energy W that swings between them, in nJ.

C = 470 pFV0 = 20 VL = 100 µH
W = nJ
2.Easy
f|I|0.7071500 kHzf1​f2​BW = 12.5 kHz

A resonance curve peaks at 500 kHz, and its half-power points are 12.5 kHz apart. Find the quality factor Q.

f0 = 500 kHzBW = 12.5 kHz
Q =
3.Medium
f|I|0.7071500 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 500 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 500 kHzQ = 2
f1 = kHz
4.Medium
V220 Ω4.7 mH4.7 nF

A series RLC circuit has R = 220 Ω, L = 4.7 mH and C = 4.7 nF. Find its quality factor Q.

R = 220 ΩL = 4.7 mHC = 4.7 nF
Q =
5.Hard
C = 2.2 nFr = 10 ΩL = 4.7 mH

A parallel tank circuit is made of a 2.2 nF 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 = 2.2 nFr = 10 Ω
RD = kΩ
6.Hard
V10 Ω47 mH47 nF10 mA

A series RLC circuit (R = 10 Ω, L = 47 mH, C = 47 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 10 ΩL = 47 mHC = 47 nFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. W = 94 nJ
  2. 2. Q = 40
  3. 3. f1 = 390.4 kHz
  4. 4. Q = 4.545
  5. 5. RD = 213.6 kΩ
  6. 6. Ecycle = 147.7 nJ

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