Question

A series-parallel combination of battery consisting of a large number $N=300$ of identical cells, each with an internal resistance $r=0.3\Omega ,$ is loaded with an external resistance $R=10\Omega$. then, the number $n$ of parallel group consisting of an equal number of cells connected in series at which the external resistance generates highest thermal power is

• A. 3
• B. 4
• C. 5
• D. none of the above

Answer 1

Answer: (A)

3

We know that when external resistance is equal to internal resistance i.e. R = r then power withdrawn from battery is maxiumum. $P_{max}=\frac{{ϵ}^2}{4R}$ using this concept ,

For $n$ rows the net eq resistance would be ,
$Req=\frac{Nr}{nn}⟹\frac{Nr}{nn}=R⟹n=\frac{rN}{R}=\frac{0.3\times 300}{10}=3$