Parallel Resonant Circuit

By Aina Parasher|Updated : July 19th, 2022

Consider the parallel resonant circuit shown below-

  1. Determine resonant frequencies ωr(rad/sec) and fr(Hz) of the circuit.
  2. Calculate the voltage across the circuit at resonance.
  3. Solve for the current through the resistor and the inductor at resonance.

Solution

For a parallel rlc circuit admittance offered by the circuit Y=G+jB=G+j(BC-BL)

Here G= conductance of resistor R

capacitive susceptance BC=ωC

inductive susceptance BL=1ωL

For a parallel resonant circuit admittance offered by the circuit Y=G

That means in parallel resonant circuit BC=BL

ωrC=1/ωrL

1. So, resonant frequency ωr=1/√L.C=1/√(0.4×10-6)(16×10-3)=12.5 ×103 rad/sec

And frr/=1989.4 Hz≈1989 Hz

2. Voltage across the circuit at resonance V=I.R

Here, from the circuit given in the problem I=3.6 mA∠0°

And resistance R=500

So, V=I.R=3.6×10-3∠0°.500=1.8∠0° V

3. Current through resistor IR=V/R=1.8∠0°/500=3.6∠0° mA

and current through inductor IL=V(-JBL)

here BL=1/ωL=1/12.5×10-3(16×10-9)=1200 siemens

IL=V(-JBL)=1.8∠0°×1/200-90°=9 mA∠-90°

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