Question

In the given circuit, the current drawn from the source is

• A. $20A$
• B. $10A$
• C. $5A$
• D. $5\sqrt{2}A$

Answer 1

The correct option is D $5\sqrt{2}A$

$\text{All the three are connected in parallel so voltage are same across them}$
$X_L=10\Omega ,X_c=20\Omega ,R=20\Omega ,V=100\text{volt}$
$\text{Current in resistor}\left(i_1\right)=\frac{V}{R}=\frac{100}{20}=5\text{A}$

$\text{Current in inductor}\left(i_2\right)=jV{X}_l=j\frac{100}{10}=10j\text{A}$

$\text{current in capacitor}\left(i_3\right)=-j\frac{V}{X_C}=-j\frac{100}{20}=-5j\text{A}$

$\text{So, total current}i=i_1+(i_2+i_3)j$
$i=5+(10-5)j=5+5j$
$\text{Therefore magnitude of current}=\sqrt{5^2+5^2}=5\sqrt{2}\text{A}$