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|0.70711.6 MHzf1​f2​BW = 80 kHz

A resonance curve peaks at 1.6 MHz, and its half-power points are 80 kHz apart. Find the quality factor Q.

f0 = 1.6 MHzBW = 80 kHz
Q =
2.Easy
C = ?L = 2.2 mH

An LC circuit with L = 2.2 mH must resonate at 50 kHz. Find the capacitance C in nF.

L = 2.2 mHf0 = 50 kHz
C = nF
3.Medium
V5 Ω10 mH10 nF

A series RLC circuit has R = 5 Ω, L = 10 mH and C = 10 nF. Find its bandwidth BW in Hz.

R = 5 ΩL = 10 mHC = 10 nF
BW = Hz
4.Medium
f|I|0.7071100 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 100 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 100 kHzQ = 3
f1 = kHz
5.Hard
VR = ?22 µHC

A series resonant circuit uses a 22 µH inductor. Which total series resistance R gives a bandwidth of 50 kHz?

L = 22 µHBW = 50 kHz
R = Ω
6.Hard
C = 10 nFr = 2 ΩL = 10 mH

A parallel tank circuit is made of a 10 nF capacitor and a 10 mH 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 = 10 mHC = 10 nFr = 2 Ω
RD = kΩ

Answer key

  1. 1. Q = 20
  2. 2. C = 4.606 nF
  3. 3. BW = 79.58 Hz
  4. 4. f1 = 84.71 kHz
  5. 5. R = 6.912 Ω
  6. 6. RD = 500 kΩ

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