Question

The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then:

• A. the resistance and the specific resistance, will both remain unchanged
• B. the resistance will be doubled and the specific resistance will be halved
• C. the resistance will be halved and the specific resistance will remain unchanged
• D. the resistance will be halved and the specific resistance will be doubled

Hint:

When both the length and radius of a wire are doubled, the resistance remains unchanged because the length and area change in opposite ways.

Answer 1

The Correct Option is A

Step 1: Resistance formula.
The resistance \( R \) of a wire is given by: \[ R = \rho \frac{L}{A} \] where \( \rho \) is the specific resistance, \( L \) is the length, and \( A \) is the cross-sectional area. Step 2: Effects of doubling the length and radius.
When the length is doubled, the new length becomes \( 2L \). The area, which is proportional to the square of the radius, becomes \( 4A \) when the radius is doubled. Therefore, the new resistance is: \[ R_{\text{new}} = \rho \frac{2L}{4A} = \frac{1}{2} \times R \] Thus, the resistance remains unchanged because both the effects of doubling the length and radius cancel each other.
Final Answer: \[ \boxed{1} \]