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 = 100 nFL = 220 µH

An ideal LC circuit has L = 220 µH and C = 100 nF. Find its natural (resonance) frequency f0 in kHz.

L = 220 µHC = 100 nF
f0 = kHz
2.Easy
C = 22 nFL = 2.2 mH

An ideal LC circuit has L = 2.2 mH and C = 22 nF. Find its natural (resonance) frequency f0 in kHz.

L = 2.2 mHC = 22 nF
f0 = kHz
3.Medium
f|I|0.70715 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 5 kHz with Q = 2. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 5 kHzQ = 2
f1 = kHz
4.Medium
V10 Ω100 mH100 nF

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

R = 10 ΩL = 100 mHC = 100 nF
BW = Hz
5.Hard
C = 4.7 nFr = 2 ΩL = 100 µH

A parallel tank circuit is made of a 4.7 nF capacitor and a 100 µH 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 = 100 µHC = 4.7 nFr = 2 Ω
RD = kΩ
6.Hard
V22 Ω10 mH47 nF10 mA

A series RLC circuit (R = 22 Ω, L = 10 mH, C = 47 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 = 22 ΩL = 10 mHC = 47 nFIm = 10 mA
Ecycle = nJ

Answer key

  1. 1. f0 = 33.93 kHz
  2. 2. f0 = 22.88 kHz
  3. 3. f1 = 3.904 kHz
  4. 4. BW = 15.92 Hz
  5. 5. RD = 10.64 kΩ
  6. 6. Ecycle = 149.8 nJ

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