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 = 10 µH

An LC circuit with L = 10 µH must resonate at 1 MHz. Find the capacitance C in nF.

L = 10 µHf0 = 1 MHz
C = nF
2.Easy
f|I|0.7071500 kHzf1​f2​BW = ?

A tuned circuit resonates at 500 kHz and has a quality factor Q = 100. Find its bandwidth BW in kHz.

f0 = 500 kHzQ = 100
BW = kHz
3.Medium
V22 Ω47 µH10 nF

A series RLC circuit has R = 22 Ω, L = 47 µH and C = 10 nF. Find its quality factor Q.

R = 22 ΩL = 47 µHC = 10 nF
Q =
4.Medium
V4.7 kΩ4.7 mH100 nF

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

R = 4.7 kΩL = 4.7 mHC = 100 nF
Q =
5.Hard
V100 ΩLC = ?

Design a series RLC filter with a total resistance of 100 Ω, a resonance frequency of 50 kHz and a bandwidth of 2.5 kHz. Find the capacitance C in nF.

R = 100 Ωf0 = 50 kHzBW = 2.5 kHz
C = nF
6.Hard
V2 Ω2.2 µH47 nF200 mA

A series RLC circuit (R = 2 Ω, L = 2.2 µH, C = 47 nF) is driven at resonance with a current amplitude of 200 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 2.2 µHC = 47 nFIm = 200 mA
Ecycle = nJ

Answer key

  1. 1. C = 2.533 nF
  2. 2. BW = 5 kHz
  3. 3. Q = 3.116
  4. 4. Q = 21.68
  5. 5. C = 1.592 nF
  6. 6. Ecycle = 80.82 nJ

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