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 = 125 Hz

A resonance curve peaks at 10 kHz, and its half-power points are 125 Hz apart. Find the quality factor Q.

f0 = 10 kHzBW = 125 Hz
Q =
2.Easy
f|I|0.70711 kHzf1​f2​BW = 20 Hz

A resonance curve peaks at 1 kHz, and its half-power points are 20 Hz apart. Find the quality factor Q.

f0 = 1 kHzBW = 20 Hz
Q =
3.Medium
C = 4.7 nF+−4 VL = 10 µHiL​

A 4.7 nF capacitor charged to 10 V oscillates with an ideal 10 µH inductor. Find the energy WL stored in the inductor at the moment the capacitor voltage is 4 V, in nJ.

C = 4.7 nFV0 = 10 VvC = 4 V
WL = nJ
4.Medium
V10 Ω1 mH47 nF

A series RLC circuit has R = 10 Ω, L = 1 mH and C = 47 nF. Find its bandwidth BW in kHz.

R = 10 ΩL = 1 mHC = 47 nF
BW = kHz
5.Hard
C = 220 pFr = 1 ΩL = 1 mH

A parallel tank circuit is made of a 220 pF capacitor and a 1 mH 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 = 1 mHC = 220 pFr = 1 Ω
RD = kΩ
6.Hard
V5 Ω1 mH1 nF100 mA

A series RLC circuit (R = 5 Ω, L = 1 mH, C = 1 nF) is driven at resonance with a current amplitude of 100 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 5 ΩL = 1 mHC = 1 nFIm = 100 mA
Ecycle = nJ

Answer key

  1. 1. Q = 80
  2. 2. Q = 50
  3. 3. WL = 197.4 nJ
  4. 4. BW = 1.592 kHz
  5. 5. RD = 4545 kΩ
  6. 6. Ecycle = 157.1 nJ

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