Question

Assertion: When a wire is stretched to three times its length, its resistance becomes 9 times

Reason: $R=\frac{\rho l}{a}$

• A. both, Assertion and Reason are true and the reason is correct explanation of the Assertion
• B. both, Assertion and Reason are true and the reason is not correct explanation of the Assertion
• C. Assertion is true, but the reason is false.
• D. Both, Assertion and reason and false

Answer 1

The correct option is A both, Assertion and Reason are true and the reason is correct explanation of the Assertion

$\begin{array}{c}\text{According to the question, wire is}\\ \text{stretched}3\text{times to its original length}\\ \text{Volume of wire is constant, so we get:}\end{array}$

$\begin{array}{c}{A}_1{L}_1=A_2{L}_2\\ A_1{L}_1=A_2\left(3L_1\right)\\ A_2=\frac{A_1}{3}\end{array}$

$\begin{array}{c}\text{Since,}R=\frac{\rho L}{A}\Rightarrow R_2=\frac{\rho \cdot \left(3L_1\right)}{A_1/3}\\ R_2=9R_1\\ \therefore \text{Both assertion \& reason is correct.}\end{array}$