Question

The resistance of a wire of any substance of length \( l \) and area of cross-section \( A \) is 4 \( \Omega \). Another wire of the same substance has length \( 2l \) and area of cross-section \( \frac{A}{2} \). Then its resistance will be

• A. 4 \( \Omega \)
• B. 8 \( \Omega \)
• C. 16 \( \Omega \)
• D. 32 \( \Omega \)

Hint:

Resistance of a wire is directly proportional to length and inversely proportional to the cross-sectional area.

Answer 1

The Correct Option is C

The resistance of a wire is given by: \[ R = \rho \frac{l}{A} \] For the original wire: \[ R_1 = \rho \frac{l}{A} = 4 \Omega \] For the second wire with length \( 2l \) and area \( \frac{A}{2} \): \[ R_2 = \rho \frac{2l}{A/2} = \rho \frac{4l}{A} = 4 \times 4 = 16 \Omega \]