Question

The circuit given below shows seven identical bulbs $(A$ to $G)$ connected through a battery of emf $200\, V$. The bulbs are rated as $200\, V , 100 \,W$. 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

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

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