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 = ?

A tuned circuit resonates at 50 kHz and has a quality factor Q = 40. Find its bandwidth BW in kHz.

f0 = 50 kHzQ = 40
BW = kHz
2.Easy
f|I|0.707110.7 MHzf1​f2​BW = ?

A tuned circuit resonates at 10.7 MHz and has a quality factor Q = 12. Find its bandwidth BW in kHz.

f0 = 10.7 MHzQ = 12
BW = kHz
3.Medium
f|I|0.70711 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 1 kHz with Q = 5. Find the lower half-power frequency f1 exactly, in Hz.

f0 = 1 kHzQ = 5
f1 = Hz
4.Medium
V47 kΩ220 µH4.7 nF

A parallel RLC circuit has R = 47 kΩ, L = 220 µH and C = 4.7 nF. Find its quality factor Q.

R = 47 kΩL = 220 µHC = 4.7 nF
Q =
5.Hard
C = 4.7 nFr = 1 ΩL = 22 µH

A parallel tank circuit is made of a 4.7 nF capacitor and a 22 µH coil with a winding resistance of 1 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 22 µHC = 4.7 nFr = 1 Ω
RD = kΩ
6.Hard
VR = ?22 mHC

A series resonant circuit uses a 22 mH inductor. Which total series resistance R gives a bandwidth of 20 kHz?

L = 22 mHBW = 20 kHz
R = Ω

Answer key

  1. 1. BW = 1.25 kHz
  2. 2. BW = 891.7 kHz
  3. 3. f1 = 905 Hz
  4. 4. Q = 217.2
  5. 5. RD = 4.681 kΩ
  6. 6. R = 2765 Ω

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