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 kHzf1​f2​BW = ?

A tuned circuit resonates at 10 kHz and has a quality factor Q = 50. Find its bandwidth BW in Hz.

f0 = 10 kHzQ = 50
BW = Hz
2.Easy
C = 220 nF+−50 VL = 22 mHiL​

A 220 nF capacitor charged to 50 V is switched across an ideal 22 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 220 nFV0 = 50 VL = 22 mH
Imax = mA
3.Medium
V1 Ω22 µH22 nF

A series RLC circuit has R = 1 Ω, L = 22 µH and C = 22 nF. Find its bandwidth BW in kHz.

R = 1 ΩL = 22 µHC = 22 nF
BW = kHz
4.Medium
C = 470 pF+−12 VL = 1 mHiL​

A 470 pF capacitor charged to 24 V oscillates with an ideal 1 mH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 12 V, in nJ.

C = 470 pFV0 = 24 VvC = 12 V
WL = nJ
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 = 22 nFr = 2 ΩL = 100 µH

A parallel tank circuit is made of a 22 nF capacitor and a 100 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 = 100 µHC = 22 nFr = 2 Ω
RD = kΩ

Answer key

  1. 1. BW = 200 Hz
  2. 2. Imax = 158.1 mA
  3. 3. BW = 7.234 kHz
  4. 4. WL = 101.5 nJ
  5. 5. R = 12.57 Ω
  6. 6. RD = 2.273 kΩ

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