A battery consists of a variable number ‘n’ of identical cells (having internal resistance ‘r’ each) which are connected in series. The terminals of the battery are short-circuited and the current I is measured. Which of the graphs shows the correct relationship between I and n ?
The Correct Option is A
Solution and Explanation
To solve this problem, consider the electrical behavior of identical cells in series.
- For n identical cells in series, total emf is: \[ E_{\text{total}} = nE \]
- Total internal resistance is: \[ R_{\text{internal}} = nr \]
- For a short circuit (external resistance = 0), current is: \[ I = \frac{E_{\text{total}}}{R_{\text{internal}}} = \frac{nE}{nr} = \frac{E}{r} \]
- Hence, current is independent of n.
Conclusion: The current remains constant as the number of cells increases, so the graph is a horizontal line.
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