Question

How does the resistance of a wire change when
a. Its length is tripled
b. Its diameter is tripled
c. Its material is changed to one whose resistivity is three times

Answer 1

Since we know the formula:

$r = \rho \frac{l}{a}$

• on tripling the length, resistance will increase by 3 times
• on tripling its diameter, radius will be tripled hence area(a=πr²) will increase by 9 times so resistance will decrease by 9 times
• since resistance directly depends on resistivity so it will also be tripled when a material of resistivity thrice as that of original is used