There are `N` cells in the circuit of figure. The emf and internal resistance of each cell is `E` and `r` respectively. The points `A` and `B` in the circuit divide the circuit into `n` and `(N-n)`cells. The current in the circuit is

Options

A. `E//r`
B. `nE//r`
C. `NE//nr`
D. zero

Explanation

To find the current in the circuit with `N` cells, each having an emf of `E` and an internal resistance of `r`, we can follow these steps:

### Step 1: Understand the Configuration
We have `N` cells in the circuit, and they are divided into two parts by points `A` and `B`. One part contains `n` cells, and the other part contains `N - n` cells.

### Step 2: Calculate the Total EMF
The total emf contributed by the `n` cells is:
\[ \text{EMF from } n \text{ cells} = n \cdot E \]
The total emf contributed by the `N - n` cells is:
\[ \text{EMF from } (N - n) \text{ cells} = (N - n) \cdot E \]
Thus, the net emf in the circuit is:
\[ \text{Net EMF} = n \cdot E + (N - n) \cdot E = N \cdot E \]

### Step 3: Calculate the Total Internal Resistance
The internal resistance contributed by the `n` cells is:
\[ \text{Resistance from } n \text{ cells} = n \cdot r \]
The internal resistance contributed by the `N - n` cells is:
\[ \text{Resistance from } (N - n) \text{ cells} = (N - n) \cdot r \]
Thus, the total internal resistance in the circuit is:
\[ \text{Total Resistance} = n \cdot r + (N - n) \cdot r = N \cdot r \]

### Step 4: Apply Ohm's Law to Find Current
Using Ohm's law, the current `I` in the circuit can be calculated as:
\[ I = \frac{\text{Net EMF}}{\text{Total Resistance}} = \frac{N \cdot E}{N \cdot r} \]
This simplifies to:
\[ I = \frac{E}{r} \]

### Final Answer
The current in the circuit is:
\[ I = \frac{E}{r} \]

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