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 = 891.7 kHz

A resonance curve peaks at 10.7 MHz, and its half-power points are 891.7 kHz apart. Find the quality factor Q.

f0 = 10.7 MHzBW = 891.7 kHz
Q =
2.Easy
C = 100 pFL = 22 mH

An ideal LC circuit has L = 22 mH and C = 100 pF. Find its natural (resonance) frequency f0 in kHz.

L = 22 mHC = 100 pF
f0 = kHz
3.Medium
V22 Ω22 mH2.2 nF

A series RLC circuit has R = 22 Ω, L = 22 mH and C = 2.2 nF. Find its quality factor Q.

R = 22 ΩL = 22 mHC = 2.2 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 22 mHC = 2.2 nF

In an ideal LC circuit with L = 22 mH and C = 2.2 nF, 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 = 22 mHC = 2.2 nF
t = µs
5.Hard
f|I|0.7071f0​ = ?50 kHz100 kHzBW

The half-power frequencies of a resonance curve are 50 kHz and 100 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 50 kHzf2 = 100 kHz
Q =
6.Hard
C = 2.2 nFr = 1 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 1 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 = 1 Ω
RD = kΩ

Answer key

  1. 1. Q = 12
  2. 2. f0 = 107.3 kHz
  3. 3. Q = 143.7
  4. 4. t = 10.93 µs
  5. 5. Q = 1.414
  6. 6. RD = 45.45 kΩ

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