Correct Answer - Option 1 : wire of cross-sectional area 2A
Concept:
The resistance offered to the flow of current is known as the resistance.
SI unit of resistance is the ohm (Ω).
Mathematically, the resistance can be written as:
\(R \propto \frac{l}{A}\)
\(R = \frac{{\rho l}}{A}\)
R = resistance
l = length
A = area of cross-section
ρ = resistivity
Calculation:
Three wires of different lengths and cross-sectional areas are given as:
(l, A), (2l, A/2), and (l/2, 2A).
For Ist wire:
R1 ∝ l / A = R
For IInd wire:
\({R_2} \propto \frac{{2l}}{{A/2}} = 4R\)
For IIIrd wire:
\({R_3} \propto \frac{{l/2}}{{2A}} = \frac{R}{4}\)
Therefore resistance of the wire will be minimum for IIIrd wire.