Question

In a parallel $L-C-R$ circuit as shown in figure if $I_R,I_L,I_C$ and $I$ represents the rms values of current flowing through resistor, inductor, capacitor and the source, 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 the above

Answer 1

Answer: (C)

$I_L$ or $I_C$ may be greater than $I$

Voltage $V$ is same across all the elements.

currents, $I_R=V/R;I_L=V/\omega L;I_C=\omega C\times I$, where $\omega$ is frequency of current source $I$

now total current is $I$ is the vector sum of three currents, and cannot be simply added like vectors. Thus option A and B are incorrect.

The vector sum $I$ can be lower than any of its $I_R,I_L,I_C$. So, option C is correct.