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 = ?

A tuned circuit resonates at 1.6 MHz and has a quality factor Q = 100. Find its bandwidth BW in kHz.

f0 = 1.6 MHzQ = 100
BW = kHz
2.Easy
C = 10 µFL = 470 µH

An ideal LC circuit has L = 470 µH and C = 10 µF. Find its natural (resonance) frequency f0 in kHz.

L = 470 µHC = 10 µF
f0 = kHz
3.Medium
V10 kΩ4.7 mH2.2 nF

A parallel RLC circuit has R = 10 kΩ, L = 4.7 mH and C = 2.2 nF. Find its quality factor Q.

R = 10 kΩL = 4.7 mHC = 2.2 nF
Q =
4.Medium
V47 kΩ47 mH22 nF

A parallel RLC circuit has R = 47 kΩ, L = 47 mH and C = 22 nF. Find its quality factor Q.

R = 47 kΩL = 47 mHC = 22 nF
Q =
5.Hard
C = 10 nFr = 20 ΩL = 100 mH

A parallel tank circuit is made of a 10 nF capacitor and a 100 mH coil with a winding resistance of 20 Ω. At resonance it behaves like a resistor, its dynamic resistance RD = L/(C·r). Find RD in kΩ.

L = 100 mHC = 10 nFr = 20 Ω
RD = kΩ
6.Hard
V10 Ω1 mH100 nF10 mA

A series RLC circuit (R = 10 Ω, L = 1 mH, C = 100 nF) is driven at resonance with a current amplitude of 10 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 10 ΩL = 1 mHC = 100 nFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. BW = 16 kHz
  2. 2. f0 = 2.322 kHz
  3. 3. Q = 6.842
  4. 4. Q = 32.16
  5. 5. RD = 500 kΩ
  6. 6. Ecycle = 31.42 nJ

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