4400 Higher June 2004 Paper 3 Q17

17 An electrician has wires of the same length made from the same material.
The electrical resistance, \(R\) ohms, of a wire is inversely proportional to the square of its radius, \(r\) mm.
When \(r = 2\), \(R = 0.9\)

(a)

(i) Express \(R\) in terms of \(r\).

(ii) On the axes, sketch the graph of \(R\) against \(r\).

(4)

One of the electrician’s wires has a radius of 3 mm.