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|0.70711 kHzf1​f2​BW = ?

A tuned circuit resonates at 1 kHz and has a quality factor Q = 100. Find its bandwidth BW in Hz.

f0 = 1 kHzQ = 100
BW = Hz
2.Easy
C = 2.2 µFL = 2.2 mH

An ideal LC circuit has L = 2.2 mH and C = 2.2 µF. Find its natural (resonance) frequency f0 in kHz.

L = 2.2 mHC = 2.2 µF
f0 = kHz
3.Medium
V10 Ω100 mH22 nF

A series RLC circuit has R = 10 Ω, L = 100 mH and C = 22 nF. Find its bandwidth BW in Hz.

R = 10 ΩL = 100 mHC = 22 nF
BW = Hz
4.Medium
V2 Ω100 µH22 nF

A series RLC circuit has R = 2 Ω, L = 100 µH and C = 22 nF. Find its quality factor Q.

R = 2 ΩL = 100 µHC = 22 nF
Q =
5.Hard
f|I|0.7071f0​ = ?900 kHz2.25 MHzBW

The half-power frequencies of a resonance curve are 900 kHz and 2.25 MHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 900 kHzf2 = 2.25 MHz
Q =
6.Hard
C = 100 nFr = 20 ΩL = 2.2 mH

A parallel tank circuit is made of a 100 nF capacitor and a 2.2 mH 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 = 2.2 mHC = 100 nFr = 20 Ω
RD = kΩ

Answer key

  1. 1. BW = 10 Hz
  2. 2. f0 = 2.288 kHz
  3. 3. BW = 15.92 Hz
  4. 4. Q = 33.71
  5. 5. Q = 1.054
  6. 6. RD = 1.1 kΩ

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