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
C = ?L = 47 µH

An LC circuit with L = 47 µH must resonate at 200 kHz. Find the capacitance C in nF.

L = 47 µHf0 = 200 kHz
C = nF
2.Easy
f|I|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 8. Find its bandwidth BW in MHz.

f0 = 10.7 MHzQ = 8
BW = MHz
3.Medium
V22 Ω1 mH1 nF

A series RLC circuit has R = 22 Ω, L = 1 mH and C = 1 nF. Find its quality factor Q.

R = 22 ΩL = 1 mHC = 1 nF
Q =
4.Medium
V22 kΩ470 µH22 nF

A parallel RLC circuit has R = 22 kΩ, L = 470 µH and C = 22 nF. Find its quality factor Q.

R = 22 kΩL = 470 µHC = 22 nF
Q =
5.Hard
C = 47 nFr = 0.5 ΩL = 220 µH

A parallel tank circuit is made of a 47 nF capacitor and a 220 µH coil with a winding resistance of 0.5 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 220 µHC = 47 nFr = 0.5 Ω
RD = kΩ
6.Hard
VR = ?470 µHC

A series resonant circuit uses a 470 µH inductor. Which total series resistance R gives a bandwidth of 1 kHz?

L = 470 µHBW = 1 kHz
R = Ω

Answer key

  1. 1. C = 13.47 nF
  2. 2. BW = 1.337 MHz
  3. 3. Q = 45.45
  4. 4. Q = 150.5
  5. 5. RD = 9.362 kΩ
  6. 6. R = 2.953 Ω

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