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 = 40 kHz

A resonance curve peaks at 1.6 MHz, and its half-power points are 40 kHz apart. Find the quality factor Q.

f0 = 1.6 MHzBW = 40 kHz
Q =
2.Easy
C = 4.7 nF+−3 VL = 22 mHiL​

A 4.7 nF capacitor charged to 3 V is switched across an ideal 22 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 4.7 nFV0 = 3 VL = 22 mH
Imax = mA
3.Medium
f|I|0.7071500 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 500 kHz with Q = 2.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 500 kHzQ = 2.5
f1 = kHz
4.Medium
tvC​iL​T/4 = ?T/2TL = 1 µHC = 47 nF

In an ideal LC circuit with L = 1 µH and C = 47 nF, the capacitor is fully charged at t = 0. How long does it take until all the energy is in the inductor? Give t in µs.

L = 1 µHC = 47 nF
t = µs
5.Hard
C = 2.2 nFr = 10 ΩL = 2.2 mH

A parallel tank circuit is made of a 2.2 nF capacitor and a 2.2 mH coil with a winding resistance of 10 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 2.2 mHC = 2.2 nFr = 10 Ω
RD = kΩ
6.Hard
C = 2.2 nFr = 1 ΩL = 470 µH

A parallel tank circuit is made of a 2.2 nF capacitor and a 470 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 = 470 µHC = 2.2 nFr = 1 Ω
RD = kΩ

Answer key

  1. 1. Q = 40
  2. 2. Imax = 1.387 mA
  3. 3. f1 = 409.9 kHz
  4. 4. t = 0.3405 µs
  5. 5. RD = 100 kΩ
  6. 6. RD = 213.6 kΩ

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