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?
Answer & explanation
Correct answer: option 2
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