Question

A metal wire has a length of 2 meters and a resistance of \( 10 \, \Omega \). If the length of the wire is doubled, while keeping the material and cross-sectional area the same, what will be the new resistance?

• A. \( 10 \, \Omega \)
• B. \( 20 \, \Omega \)
• C. \( 40 \, \Omega \)
• D. \( 5 \, \Omega \)

Hint:

The resistance of a wire is directly proportional to its length. Doubling the length of a wire doubles its resistance, provided the material and cross-sectional area remain the same.

Answer 1

The Correct Option is B

The resistance \( R \) of a wire is given by the formula: \[ R = \rho \frac{L}{A} \] Where: - \( R \) is the resistance, - \( \rho \) is the resistivity of the material (constant), - \( L \) is the length of the wire, - \( A \) is the cross-sectional area of the wire. Since the material and cross-sectional area of the wire are unchanged, the resistance is directly proportional to the length of the wire. If the length of the wire is doubled, the new resistance will be twice the original resistance. Let the original resistance be \( R_1 = 10 \, \Omega \) and the original length be \( L_1 = 2 \, \text{m} \). When the length is doubled, the new length becomes \( L_2 = 2 \times L_1 = 4 \, \text{m} \). The new resistance \( R_2 \) will be: \[ R_2 = 2 \times R_1 = 2 \times 10 = 20 \, \Omega \] Thus, the new resistance is \( 20 \, \Omega \).