Question

The circuit given below shows seven identical bulbs $(A$ to $G)$ connected through a battery of emf $200V$. The bulbs are rated as $200V,100W$. The power dissipated in the bulb which glows brightest is given by $P$ watt. Find the value of $\frac{2}{3}\sqrt{P}$.

Answer 1

Answer: 5

In the given circuit, bulb $D$ glows brightest.

$R=\frac{(200{)}^2}{100}$
$i_2=\frac{200}{\left(\frac{4R}{3}\right)}$
Power in bulb $D,P=i_2^{2}R$
$\Rightarrow P={\left(\frac{200}{\frac{4R}{3}}\right)}^2\times R$
$=\frac{9}{16}\cdot \frac{(200{)}^2}{\frac{(200{)}^2}{100}}=\frac{900}{16}W$
$\Rightarrow \frac{2}{3}\sqrt{P}=\frac{2}{3}\sqrt{\frac{900}{16}}=5$