Question

In the circuit shown in the figure, $X_C=100\Omega ,X_L=200\Omega$ and $R=100\Omega$. The effective current through the source is

• A. $2\text{A}$
• B. $2\sqrt{2}\text{A}$
• C. $0.5\text{A}$
• D. $\sqrt{0.4}\text{A}$

Answer 1

The correct option is B $2\sqrt{2}\text{A}$

Let $i_1$ be the current through $R$ and $i_2$ be the current through $L$ and $C$.


$\therefore i_1=\frac{200}{R}=\frac{200}{100}=2\text{A}$

And, $i_2=\frac{200}{X_L-X_C}=\frac{200}{100}=2\text{A}$

Now, the Phasor diagram would look like


$\therefore i_{net}=\sqrt{i_1^2+i_2^2}$

$\Rightarrow i_{net}=\sqrt{2^2+2^2}$

$\Rightarrow i_{net}=2\sqrt{2}\text{A}$

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