Consider `N=n_(1)n_(2)`indentical cells, each of emf`(epsilon)` and internal resistance r. Suppose `n_(1)` cells are joined in series to forn a line and n_(2) such are connected in parallel. The combination drives a current in an external resistance R.(a) find the current in the external resistance, (b) Assuming that `n_(1)`and n_(2) can be continuously varied, find the relation between `n_(1) ,n_(2) R and r for which the current in R in maximum.

Explanation

To solve the problem step by step, we will break it down into two parts as per the question.

### Part (a): Finding the current in the external resistance R

1. **Understanding the Configuration**:
- We have `n1` cells connected in series. The total emf from these cells is:
\[
V_{AB} = n1 \cdot \epsilon
...