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
C = 470 nF+−50 VL = 47 mHiL​

A 470 nF capacitor charged to 50 V is switched across an ideal 47 mH inductor. Find the peak current Imax in the circuit, in mA.

C = 470 nFV0 = 50 VL = 47 mH
Imax = mA
2.Easy
f|I|0.707110.7 MHzf1​f2​BW = 891.7 kHz

A resonance curve peaks at 10.7 MHz, and its half-power points are 891.7 kHz apart. Find the quality factor Q.

f0 = 10.7 MHzBW = 891.7 kHz
Q =
3.Medium
V47 kΩ47 mH2.2 nF

A parallel RLC circuit has R = 47 kΩ, L = 47 mH and C = 2.2 nF. Find its quality factor Q.

R = 47 kΩL = 47 mHC = 2.2 nF
Q =
4.Medium
tvC​iL​T/4 = ?T/2TL = 100 µHC = 10 nF

In an ideal LC circuit with L = 100 µH and C = 10 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 = 100 µHC = 10 nF
t = µs
5.Hard
C = 47 nFr = 10 ΩL = 2.2 mH

A parallel tank circuit is made of a 47 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 = 47 nFr = 10 Ω
RD = kΩ
6.Hard
V5 Ω47 µH100 nF500 mA

A series RLC circuit (R = 5 Ω, L = 47 µH, C = 100 nF) is driven at resonance with a current amplitude of 500 mA. Find the energy Ecycle dissipated in R during one cycle, in µJ.

R = 5 ΩL = 47 µHC = 100 nFIm = 500 mA
Ecycle = µJ

Answer key

  1. 1. Imax = 158.1 mA
  2. 2. Q = 12
  3. 3. Q = 10.17
  4. 4. t = 1.571 µs
  5. 5. RD = 4.681 kΩ
  6. 6. Ecycle = 8.514 µJ

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