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 = 1 µFL = 0.1 µH

An ideal LC circuit has L = 0.1 µH and C = 1 µF. Find its natural (resonance) frequency f0 in kHz.

L = 0.1 µHC = 1 µF
f0 = kHz
2.Easy
C = 4.7 nF+−50 VL = 1 mHiL​

A 4.7 nF capacitor charged to 50 V is switched across an ideal 1 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 4.7 nFV0 = 50 VL = 1 mH
Imax = mA
3.Medium
V100 kΩ100 mH4.7 nF

A parallel RLC circuit has R = 100 kΩ, L = 100 mH and C = 4.7 nF. Find its quality factor Q.

R = 100 kΩL = 100 mHC = 4.7 nF
Q =
4.Medium
V2 Ω47 µH2.2 µF

A series RLC circuit has R = 2 Ω, L = 47 µH and C = 2.2 µF. Find its quality factor Q.

R = 2 ΩL = 47 µHC = 2.2 µF
Q =
5.Hard
C = 220 pFr = 10 ΩL = 4.7 mH

A parallel tank circuit is made of a 220 pF capacitor and a 4.7 mH coil with a winding resistance of 10 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 4.7 mHC = 220 pFr = 10 Ω
RD = kΩ
6.Hard
f|I|0.7071f0​ = ?5 kHz6 kHzBW

The half-power frequencies of a resonance curve are 5 kHz and 6 kHz. Find the resonance frequency as their geometric mean, and then the quality factor Q.

f1 = 5 kHzf2 = 6 kHz
Q =

Answer key

  1. 1. f0 = 503.3 kHz
  2. 2. Imax = 108.4 mA
  3. 3. Q = 21.68
  4. 4. Q = 2.311
  5. 5. RD = 2136 kΩ
  6. 6. Q = 5.477

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