Area of cross section of a wire (A) is twice of (B) (given the wires are of the same length and of same material) then whose resistance will be?

wire B

The correct answer is option 2. wire B.

To determine which wire has higher resistance, let’s use the formula for the resistance of a wire:

\(R = \frac{\rho L}{A}\)

where:

\( R \) is the resistance of the wire,

\( \rho \) is the resistivity of the material (which is the same for both wires),

\( L \) is the length of the wire (which is also the same for both wires),

\( A \) is the cross-sectional area of the wire.

Given:

Wire A has a cross-sectional area \( A_A \),

Wire B has a cross-sectional area \( A_B \),

\( A_A = 2A_B \),

The wires are of the same length and material.

Using the resistance formula:

For Wire A:

\(R_A = \frac{\rho L}{A_A}\)

For Wire B:

\(R_B = \frac{\rho L}{A_B}\)

Since \( A_A = 2A_B \):

\(R_A = \frac{\rho L}{2A_B}\)

Comparing the resistances:

\(R_A = \frac{1}{2} \times \frac{\rho L}{A_B} = \frac{1}{2} R_B\)

This shows that the resistance of Wire A is half that of Wire B.

Conclusion

Wire B, with the smaller cross-sectional area, has higher resistance compared to Wire A.

So the correct answer is: 2. Wire B