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Assertion: Two identical cells of emf E ...

Assertion: Two identical cells of emf E and internal resistance r are connected to each other in such a manner that the positive terminal of one is connected to the positive terminal of the other. The net emf of its combination will be E.
Reason: Effective internal resistance of this combination will be `r//2`

A

If both assertion and reason are correct and reason is a correct explanation of the assertion

B

If both assertion and reason are correct but reason is not the correct explanation of the assertion

C

If assertion is correct but reason is incorrect

D

If assertion is incorrect but reason is correct

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and reason provided regarding the combination of two identical cells. ### Step-by-Step Solution: 1. **Understanding the Configuration**: - We have two identical cells, each with an EMF (E) and internal resistance (r). - The cells are connected in such a way that the positive terminal of one cell is connected to the positive terminal of the other cell. This configuration is essentially a parallel connection. 2. **Net EMF Calculation**: - In a parallel connection of identical cells, the net EMF (E_net) remains the same as the EMF of one cell. Therefore, the net EMF of the combination is: \[ E_{\text{net}} = E \] - This confirms that the assertion is true: "The net EMF of its combination will be E." 3. **Effective Internal Resistance Calculation**: - The internal resistances of the two cells are also in parallel. The formula for the equivalent resistance (R_eq) of two resistors (r) in parallel is given by: \[ \frac{1}{R_{\text{eq}}} = \frac{1}{r} + \frac{1}{r} = \frac{2}{r} \] - Therefore, the equivalent internal resistance is: \[ R_{\text{eq}} = \frac{r}{2} \] - This confirms that the effective internal resistance of the combination is \( R/2 \), which supports the reason provided. 4. **Conclusion**: - Both the assertion and the reason are true: - The assertion is true because the net EMF of the combination is E. - The reason is true because the effective internal resistance of the combination is \( R/2 \). - However, the reason does not explain the assertion directly, as the assertion is based on the nature of EMF in parallel connections, while the reason is based on the calculation of internal resistance. ### Final Answer: - The assertion is true, and the reason is true, but the reason does not explain the assertion. Therefore, the correct option is that both are true, but they do not explain each other.
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