Question

The resistance of the conductor is R. If its length is doubled and Area is halved, then its new resistance will be
(a) R (b) 2R (c) 4R (d) 8R

Answer 1

Answer: 4R (c)

Explanation:

Given that,

Resistance of a conductor = R

Assume that it's length is = L

And area = A and resistivity = ρ.

Therefore,

R = ρL/A ___(A)

Now,

Length = 2L

Area = A/2

Hence, R′ = ρ(2L)/(A/2) = 2ρ(2L)/(A) = 4(ρL/A)

[Resistivity won't change as conductor isn't changed.]

=> R′ = 4R

Shortcuts:

• When length is changed, i.e., became L1 to L2, resistance becomes = (L2/L1)²R.
• When area becomes A1 to A2, R′ = (A1/A2)²R.
• When radius of a circular conductor becomes r2 from r1, then: R′ = (r1/r2)⁴R.