Question

A wire of length L and resistance R is stretched so that the length is doubled and area of cross –

section halved. How will

(i) resistance change, and

(ii) resistivity change​

Answer 1

Explanation:

R = ρ*l/A

where R is resistance in ohm, ρ is resistivity in ohm-meter, l is length in meter & A is cross sectional area in m^2

Since the current becomes ‘2l’ & the ‘A’ becomes ‘A/2’, so the new resistance will be,

R’ = ρ*2l/(A/2)

or, R’ = ρ*2*2*l/A

or, R’ = 4*ρ*l/A

or, R’ = 4R

So the new resistance will be 4 times than previous.

Coming to your second question, Resistivity cannot be changed for a same material. It is constant term. Every material has their own fixed resistivity.