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 = 2.2 µFL = 47 µH

An ideal LC circuit has L = 47 µH and C = 2.2 µF. Find its natural (resonance) frequency f0 in kHz.

L = 47 µHC = 2.2 µF
f0 = kHz
2.Easy
C = ?L = 10 mH

An LC circuit with L = 10 mH must resonate at 200 kHz. Find the capacitance C in nF.

L = 10 mHf0 = 200 kHz
C = nF
3.Medium
V5 Ω100 mH47 nF

A series RLC circuit has R = 5 Ω, L = 100 mH and C = 47 nF. Find its bandwidth BW in Hz.

R = 5 ΩL = 100 mHC = 47 nF
BW = Hz
4.Medium
V2 Ω2.2 µH100 nF

A series RLC circuit has R = 2 Ω, L = 2.2 µH and C = 100 nF. Find its quality factor Q.

R = 2 ΩL = 2.2 µHC = 100 nF
Q =
5.Hard
C = 4.7 nFr = 0.5 ΩL = 2.2 mH

A parallel tank circuit is made of a 4.7 nF capacitor and a 2.2 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 = 2.2 mHC = 4.7 nFr = 0.5 Ω
RD = kΩ
6.Hard
f|I|0.7071f0​ = ?100 kHz160 kHzBW

The half-power frequencies of a resonance curve are 100 kHz and 160 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 100 kHzf2 = 160 kHz
Q =

Answer key

  1. 1. f0 = 15.65 kHz
  2. 2. C = 0.06333 nF
  3. 3. BW = 7.958 Hz
  4. 4. Q = 2.345
  5. 5. RD = 936.2 kΩ
  6. 6. Q = 2.108

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