Question

A sinusoidal voltage of peak value $283\, V$ and frequency $50\, Hz$ is applied to a series $L-C-R$ circuit in which $R=3\, \Omega, L=25.48\, mH$ and $C=796\, \mu F$.
Calculate the impedance, the current and the power dissipated at the resonant condition.

• A. $4\, \Omega, 13.35\, A , 60\, W$
• B. $2\, \Omega, 65\, A , 13\, kW$
• C. $8\, \Omega, 66.7\, A , 13.35\, kW$
• D. $3\, \Omega, 66.7\, A , 13.35\, kW$

Answer 1

Answer: (D)

The impedance $Z$ at resonant condition is equal to the resistance
$Z=R=3\, \Omega$
The rms current at resonance is
$=\frac{V}{Z}=\frac{V}{R}=\left(\frac{283}{\sqrt{2}}\right) \frac{1}{3}=66.7\, A$
The power dissipated at resonance is
$P=I^{2} \times R=(66.7)^{2} \times 3=13.35\, kW$.