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|0.707150 kHzf1​f2​BW = ?

A tuned circuit resonates at 50 kHz and has a quality factor Q = 100. Find its bandwidth BW in Hz.

f0 = 50 kHzQ = 100
BW = Hz
2.Easy
C = 47 nFL = 100 mH

An ideal LC circuit has L = 100 mH and C = 47 nF. Find its natural (resonance) frequency f0 in kHz.

L = 100 mHC = 47 nF
f0 = kHz
3.Medium
f|I|0.7071100 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 100 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 100 kHzQ = 1.5
f1 = kHz
4.Medium
V220 Ω100 mH100 pF

A series RLC circuit has R = 220 Ω, L = 100 mH and C = 100 pF. Find its quality factor Q.

R = 220 ΩL = 100 mHC = 100 pF
Q =
5.Hard
C = 4.7 nFr = 0.5 ΩL = 1 mH

A parallel tank circuit is made of a 4.7 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 = 4.7 nFr = 0.5 Ω
RD = kΩ
6.Hard
f|I|0.7071f0​ = ?2 kHz2.5 kHzBW

The half-power frequencies of a resonance curve are 2 kHz and 2.5 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 2 kHzf2 = 2.5 kHz
Q =

Answer key

  1. 1. BW = 500 Hz
  2. 2. f0 = 2.322 kHz
  3. 3. f1 = 72.08 kHz
  4. 4. Q = 143.7
  5. 5. RD = 425.5 kΩ
  6. 6. Q = 4.472

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