Question

Resistance of a wire of length 'l' and area of cross section 'a' is found to be 10 ohm.what will be the resistance and resistivity of the new wire of the same material if its length is doubled and area of cross section is halved

Answer 1

Dear Student

Case I.
Length = l
Area = a
Resistance = 10 Ohm

R = p L/A
p l/a= 10

​​​​​​Case II.
Length = 2l
Area = a/2
R = p L/A
R = p 2l/(a/2)
R = p 4l/a
R = 4 (p l/a)
Now, p l/a = 10

Put the value in the above equation,
R = 4 x 10 = 40 Ohm
New Resistance = 40 Ohm

Resistivity will remain same. Resistivity depends on the nature of material not on length and cross sectional area.

Regards