Question

A bulb having voltage rating $V$ and power rating $W$ is supplied with current from $n$ cells each of $1.5Volt$ and internal resistance $r$. The value of $n$ to run lamp at rated power $W$ is

• A. $\frac{V^2}{(1.5V-rW)}$
• B. $\frac{V^2}{\left(rW\right)}$
• C. $\frac{(1.5V-rW)}{V^2}$
• D. $\frac{V^2}{\left(1.5V\right)}$

Answer 1

Answer: (A)

$\frac{V^2}{(1.5V-rW)}$

Let the resistance of the bulb be $R$.

Then$,R=\frac{V^2}{W}$
Let say the current be $I$. Then using $P=V\times I$
We have,
$Current=I=\frac{nE}{nr+R}=\frac{nE}{nr+\frac{V^2}{W}}$
$W=\frac{VnE}{nr+\frac{V^2}{W}}$,
Solving for $n,$
$n=\frac{V^2}{VE-rW}=\frac{V^2}{1.5V-rW}$