Question

Current provided by a battery is maximum when:

• A. internal resistance is equal to external resistance
• B. internal resistance is greater than external resistance
• C. internal resistance is less than external resistance
• D. none of the above

Answer 1

Answer: (A)

internal resistance is equal to external resistance

Answer 2

Let $n$ cells are connected in series, and such $m$ series are connected in parallel. Let the emf of each cell be $E$ and the internal resistance be $r$.This battery of cells is sending current in an external resistance $R$. Then current in the external circuit be $i$, then $i=\frac{m n E}{n r+m R}$ It is clear from this equation, that for current to be maximum the value of $(n r+m R)$ should be minimum. i.e., $n r+m R=[\sqrt{n r}-\sqrt{m R}]^{2}+2 \sqrt{m n R r}$ It's minimum value is zero. i.e., $[\sqrt{n r}-\sqrt{m R}]^{2}=0$ $\sqrt{n r}-\sqrt{m R}=0$ $n r=m R$ $R=\frac{n r}{m}$ but $\frac{n r}{m}$ is the internal resistance of the whole battery. Thus, current is maximum when the internal resistance of battery is equal to external resistance.