If n identicals cells, each of emf E and internal resistance r, are connected in series. If two ends of this combination of cells are joined to each other without any external resistance. What will be the terminal potential difference across each cell?

Options

A. E
B. E/n
C. zero
D. cannot be determine

Explanation

To solve the problem, we need to analyze the situation where \( n \) identical cells, each with an electromotive force (emf) \( E \) and internal resistance \( r \), are connected in series and then short-circuited (i.e., their ends are connected directly to each other without any external resistance).

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have \( n \) identical cells connected in series.
- Each cell has an emf \( E \) and an internal resistance \( r \).
- When connected in series, the total emf of the combination is \( nE \) (since the emfs add up).

2. **Calculating Total Internal Resistance**:
- The total internal resistance of the series combination is \( nr \) (since resistances in series add up).

3. **Short-Circuit Condition**:
- When the two ends of the combination are joined together without any external resistance, it creates a short circuit.
- In this case, the total voltage across the combination is \( nE \), and the total resistance is \( nr \).

4. **Calculating the Current**:
- According to Ohm's Law, the current \( I \) flowing through the circuit can be calculated using the formula:
\[ I = \frac{V}{R} = \frac{nE}{nr} = \frac{E}{r} \]
- Here, \( V \) is the total voltage \( nE \) and \( R \) is the total resistance \( nr \).

5. **Finding Terminal Potential Difference Across Each Cell**:
- The terminal potential difference \( V \) across each cell can be calculated using the formula:
\[ V = E - I \cdot r \]
- Substituting the value of \( I \):
\[ V = E - \left(\frac{E}{r}\right) \cdot r = E - E = 0 \]
- Therefore, the terminal potential difference across each cell is \( 0 \).

### Final Answer:
The terminal potential difference across each cell is \( 0 \).

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