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
f|I|0.707110.7 MHzf1​f2​BW = 133.8 kHz

A resonance curve peaks at 10.7 MHz, and its half-power points are 133.8 kHz apart. Find the quality factor Q.

f0 = 10.7 MHzBW = 133.8 kHz
Q =
2.Easy
C = ?L = 4.7 mH

An LC circuit with L = 4.7 mH must resonate at 500 kHz. Find the capacitance C in nF.

L = 4.7 mHf0 = 500 kHz
C = nF
3.Medium
V10 Ω470 µH10 nF

A series RLC circuit has R = 10 Ω, L = 470 µH and C = 10 nF. Find its bandwidth BW in kHz.

R = 10 ΩL = 470 µHC = 10 nF
BW = kHz
4.Medium
tvC​iL​T/4 = ?T/2TL = 10 µHC = 1 µF

In an ideal LC circuit with L = 10 µH and C = 1 µF, 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 = 10 µHC = 1 µF
t = µs
5.Hard
C = 220 nFr = 0.5 ΩL = 1 mH

A parallel tank circuit is made of a 220 nF capacitor and a 1 mH 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 = 1 mHC = 220 nFr = 0.5 Ω
RD = kΩ
6.Hard
C = 470 pFr = 1 ΩL = 4.7 mH

A parallel tank circuit is made of a 470 pF capacitor and a 4.7 mH coil with a winding resistance of 1 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 4.7 mHC = 470 pFr = 1 Ω
RD = kΩ

Answer key

  1. 1. Q = 80
  2. 2. C = 0.02156 nF
  3. 3. BW = 3.386 kHz
  4. 4. t = 4.967 µs
  5. 5. RD = 9.091 kΩ
  6. 6. RD = 10000 kΩ

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