Question

In a parallel $LCR$ circuit as shown in figure, if $I_R,I_L,I_C$ and $I$ represent the $rms$ values of current flowing through resistor, inductor, capacitor and the source respectively, then choose the appropriate correct answer.

• A. $I=I_R+I_L+I_C$
• B. $I=I_R+I_L-I_C$
• C. $I_L$ or $I_C$ may be greater than $I$
• D. None of these

Answer 1

The correct option is C $I_L$ or $I_C$ may be greater than $I$

As the resistor, the inductor and the capacitor are in parallel combination. Therefore, the voltage across all three is the same and is equal to the voltage of the source.

For resistor, the current and the voltage are in the same phase.

For inductor, the current lags the voltage by $\frac{\pi }{2}$

For capacitor, the current leads the voltage by $\frac{\pi }{2}$

The phasor diagram for the given parallel $LCR$ circuit is




Therefore, from phasor diagram

$I^2=I_R^2+(I_C-I_L{)}^2$

So, $I_C$ or $I_L$ might be greater than $I$.

Hence, option $\left(\text{C}\right)$ is correct.