Question

How is the resistance of a wire affected if a) Its length is doubled b) Its area is doubled c) Its radius is doubled

Answer 1

Explanation:

resistance= rho X length/area of cross-section

so, resistance is directly proportional to length and if the length is doubled the resistance gets doubled as well

b) resistance is inversely proportional to the area of cross-section so if area is doubled, the resistance is halved

c) R1=¶ l/2πr1

R2=¶ X l/2π2r1

or, R2=¶X l/4πr1

or, R2=(1/2)X R1

Answer 2

We know that,

R = p l/A

Here, R = resistance, p = rho (resistivity), l = length and A = area of cross section.

a) If length is doubled

l = 2l

So,

R = p (2l)/A

If the length of the wire is doubled then, resistance also becomes double.

( As resistance is directly proportional to length. So, with an increase in length resistance also increase. )

b) If the area is doubled

A = 2A

So,

R = p l/(2A)

R = 1/2 (pl)A

If the area is doubled then resistance gets halved of the original resistance.

( As resistance is inversely proportional to area. So, with an increase in area, the resistance of the wire decreases. )

c) If the radius is doubled

r = 2r

We know that A = πr²

R = p l/(πr²)

As r = 2r So, r² = 4r²

R = p l/π4r²)

R = 1/4 (pl)/(πr²)

R = 1/4 (pl)/A

If the radius of doubled then resistance becomes 4 times the original resistance.