In each of the following questions, a statement of Assertion (A) is given followed by a corresponding statement of Reason (R) just below it. Of the statement mark the correct answer.
(A) : When a wire is stretched to three times its length, its resistance becomes 9 times.
(R) : Resistance of a given wire is directly proportional to its length.

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Both ‘A’ and ‘R’ are true and ‘R’ is the correct explanation of ‘A’.

‘A’ is false and ‘R’ is true

Both ‘A’ and ‘R’ are true and ‘R’ is not the correct explanation of ‘A’

‘A’ is true and ‘R’ is false

answer is B.

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Detailed Solution

According to the question, the wire is stretched 3 times to its original length Volume of the wire is constant, so we get:

$A_{1} L_{1} = A_{2} L_{2}; A_{1} L_{1} = A_{2} (3 L_{1}); A_{2} = A_{1} / 3$

Since, $R = ρ \frac{L}{A}$

$R_{2} = ρ \frac{3 L_{1}}{A_{1} / 3} \Rightarrow R_{2} = 9 R_{1}$

∴ Both assertion & reason is correct. But R is not the correct explanation of A

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