Question

A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10⁻⁸ Ω m. What will be the length of this wire to make its resistance 10 Ω? How much does the resistance change if the diameter is doubled?

Answer 1

Resistance (R) of a copper wire of length l and cross-section A is given by the expression,

Where,

Resistivity of copper,

Area of cross-section of the wire, A =

Diameter= 0.5 mm = 0.0005 m

Resistance, R = 10 Ω

Hence, length of the wire,

If the diameter of the wire is doubled, new diameter

Therefore, resistance

Therefore, the length of the wire is 122.7 m and the new resistance is