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|0.707110.7 MHzf1​f2​BW = 1.07 MHz

A resonance curve peaks at 10.7 MHz, and its half-power points are 1.07 MHz apart. Find the quality factor Q.

f0 = 10.7 MHzBW = 1.07 MHz
Q =
2.Easy
f|I|0.70715 kHzf1​f2​BW = ?

A tuned circuit resonates at 5 kHz and has a quality factor Q = 50. Find its bandwidth BW in Hz.

f0 = 5 kHzQ = 50
BW = Hz
3.Medium
f|I|0.7071500 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 500 kHz with Q = 4. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 500 kHzQ = 4
f1 = kHz
4.Medium
V100 Ω2.2 mH1 nF

A series RLC circuit has R = 100 Ω, L = 2.2 mH and C = 1 nF. Find its bandwidth BW in kHz.

R = 100 ΩL = 2.2 mHC = 1 nF
BW = kHz
5.Hard
C = 2.2 nFr = 2 ΩL = 22 µH

A parallel tank circuit is made of a 2.2 nF capacitor and a 22 µH coil with a winding resistance of 2 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 22 µHC = 2.2 nFr = 2 Ω
RD = kΩ
6.Hard
V1 Ω100 µH2.2 µF50 mA

A series RLC circuit (R = 1 Ω, L = 100 µH, C = 2.2 µF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 1 ΩL = 100 µHC = 2.2 µFIm = 50 mA
Ecycle = nJ

Answer key

  1. 1. Q = 10
  2. 2. BW = 100 Hz
  3. 3. f1 = 441.4 kHz
  4. 4. BW = 7.234 kHz
  5. 5. RD = 5 kΩ
  6. 6. Ecycle = 116.5 nJ

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