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.

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1.Easy
tvC​iL​T/4T/2TV0​ = 9 VC = 220 pF

A 220 pF capacitor is charged to 9 V and then connected to an ideal 2.2 mH inductor. Find the total energy W that swings between them, in nJ.

C = 220 pFV0 = 9 VL = 2.2 mH
W = nJ
2.Easy
f|I|0.70711 MHzf1​f2​BW = 200 kHz

A resonance curve peaks at 1 MHz, and its half-power points are 200 kHz apart. Find the quality factor Q.

f0 = 1 MHzBW = 200 kHz
Q =
3.Medium
V47 kΩ10 mH100 pF

A parallel RLC circuit has R = 47 kΩ, L = 10 mH and C = 100 pF. Find its quality factor Q.

R = 47 kΩL = 10 mHC = 100 pF
Q =
4.Medium
V47 Ω4.7 mH4.7 nF

A series RLC circuit has R = 47 Ω, L = 4.7 mH and C = 4.7 nF. Find its quality factor Q.

R = 47 ΩL = 4.7 mHC = 4.7 nF
Q =
5.Hard
C = 2.2 nFr = 20 ΩL = 100 µH

A parallel tank circuit is made of a 2.2 nF capacitor and a 100 µH 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 = 100 µHC = 2.2 nFr = 20 Ω
RD = kΩ
6.Hard
VR = ?100 µHC

A series resonant circuit uses a 100 µH inductor. Which total series resistance R gives a bandwidth of 500 Hz?

L = 100 µHBW = 500 Hz
R = Ω

Answer key

  1. 1. W = 8.91 nJ
  2. 2. Q = 5
  3. 3. Q = 4.7
  4. 4. Q = 21.28
  5. 5. RD = 2.273 kΩ
  6. 6. R = 0.3142 Ω

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