Two wires are made having same length l and area of cross-section A. Wire 1 is made of copper and wire 2 is made of aluminium. It is given that the electrical conductivity of copper is more than that of aluminium. In this context, which one of the following statements is correct ?
- AThe resistance of wire 1 will be higher than that of wire 2.
- BThe resistance of wire 2 will be higher than that of wire 1.
- CThe resistance of both the wires will be the same.
- DIf same current is flown through both the wires, the power dissipated in both the wires will be the same.
Explanation
Resistance is given by R = ρl/A = l/(σA), so for identical length and cross-sectional area, resistance is inversely proportional to electrical conductivity σ. Copper's conductivity exceeds aluminium's, so the copper wire (wire 1) has the lower resistance and the aluminium wire (wire 2) the higher resistance. With the same current, power dissipated (I²R) would be greater in wire 2, ruling out the last option. The resistance of wire 2 is therefore higher than that of wire 1.