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|0.707150 kHzf1​f2​BW = 2.5 kHz

A resonance curve peaks at 50 kHz, and its half-power points are 2.5 kHz apart. Find the quality factor Q.

f0 = 50 kHzBW = 2.5 kHz
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|0.70712 kHzf1​ = ?f2​BW

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

f0 = 2 kHzQ = 2
f1 = kHz
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 = ?1 mHC

A series resonant circuit uses a 1 mH inductor. Which total series resistance R gives a bandwidth of 2 kHz?

L = 1 mHBW = 2 kHz
R = Ω
6.Hard
C = 2.2 nFr = 5 ΩL = 4.7 mH

A parallel tank circuit is made of a 2.2 nF capacitor and a 4.7 mH coil with a winding resistance of 5 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 4.7 mHC = 2.2 nFr = 5 Ω
RD = kΩ

Answer key

  1. 1. Q = 20
  2. 2. BW = 100 Hz
  3. 3. f1 = 1.562 kHz
  4. 4. f1 = 84.71 kHz
  5. 5. R = 12.57 Ω
  6. 6. RD = 427.3 kΩ

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