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 = ?L = 0.47 µH

An LC circuit with L = 0.47 µH must resonate at 1 MHz. Find the capacitance C in nF.

L = 0.47 µHf0 = 1 MHz
C = nF
2.Easy
f|I|0.707150 kHzf1​f2​BW = 5 kHz

A resonance curve peaks at 50 kHz, and its half-power points are 5 kHz apart. Find the quality factor Q.

f0 = 50 kHzBW = 5 kHz
Q =
3.Medium
V1 kΩ220 µH2.2 µF

A parallel RLC circuit has R = 1 kΩ, L = 220 µH and C = 2.2 µF. Find its quality factor Q.

R = 1 kΩL = 220 µHC = 2.2 µF
Q =
4.Medium
f|I|0.70711 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 1 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in Hz.

f0 = 1 kHzQ = 2
f1 = Hz
5.Hard
V22 Ω10 mH2.2 µF10 mA

A series RLC circuit (R = 22 Ω, L = 10 mH, C = 2.2 µF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 22 ΩL = 10 mHC = 2.2 µFIm = 10 mA
Ecycle = µJ
6.Hard
V2 Ω2.2 mH2.2 µF20 mA

A series RLC circuit (R = 2 Ω, L = 2.2 mH, C = 2.2 µF) is driven at resonance with a current amplitude of 20 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 2.2 mHC = 2.2 µFIm = 20 mA
Ecycle = nJ

Answer key

  1. 1. C = 53.89 nF
  2. 2. Q = 10
  3. 3. Q = 100
  4. 4. f1 = 780.8 Hz
  5. 5. Ecycle = 1.025 µJ
  6. 6. Ecycle = 174.8 nJ

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