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|0.7071455 kHzf1​f2​BW = ?

A tuned circuit resonates at 455 kHz and has a quality factor Q = 5. Find its bandwidth BW in kHz.

f0 = 455 kHzQ = 5
BW = kHz
2.Easy
tvC​iL​T/4T/2TV0​ = 3 VC = 1 nF

A 1 nF capacitor is charged to 3 V and then connected to an ideal 4.7 mH inductor. Find the total energy W that swings between them, in nJ.

C = 1 nFV0 = 3 VL = 4.7 mH
W = nJ
3.Medium
f|I|0.7071500 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 500 kHz with Q = 1.5. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 500 kHzQ = 1.5
f1 = kHz
4.Medium
V100 Ω10 mH4.7 nF

A series RLC circuit has R = 100 Ω, L = 10 mH and C = 4.7 nF. Find its bandwidth BW in kHz.

R = 100 ΩL = 10 mHC = 4.7 nF
BW = kHz
5.Hard
V22 Ω47 µH4.7 nF50 mA

A series RLC circuit (R = 22 Ω, L = 47 µH, C = 4.7 nF) is driven at resonance with a current amplitude of 50 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 22 ΩL = 47 µHC = 4.7 nFIm = 50 mA
Ecycle = nJ
6.Hard
C = 47 nFr = 2 ΩL = 4.7 mH

A parallel tank circuit is made of a 47 nF capacitor and a 4.7 mH 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 = 4.7 mHC = 47 nFr = 2 Ω
RD = kΩ

Answer key

  1. 1. BW = 91 kHz
  2. 2. W = 4.5 nJ
  3. 3. f1 = 360.4 kHz
  4. 4. BW = 1.592 kHz
  5. 5. Ecycle = 81.21 nJ
  6. 6. RD = 50 kΩ

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