Question

The electrical resistance of a conductor is 18 ohm. If the units of mass and length are doubled and the
unit of time and current also doubled, then electrical resistance become 18x units. Find take
dimension of resistivity as M'TA)​

Answer 1

Answer:

the resistance will be halved and the specific resistance will remain unchanged

Answer 2

Given:

R =  18 Ω

To find:

1) x =?

2) dimension of resistivity =?

Explanation:

The electrical resistance of a conductor is 18 Ω.

But the electrical resistance is given by

R = ρ $\frac{l}{A}$        ...(1)

R =  18 Ω

So the resistance of a conductor is directly proportional to the length of a conductor & inversely proportional to the cross-sectional area of a conductor.

If the units of mass and length are doubled and the unit of time and current also doubled, then electrical resistance becomes 18x units.

i.e. l' = 2l, m' = 2m, R' = 18R

Put these values in eq (1)

18 x =C $\frac{2l}{A}$

       = 2 ρ $\frac{l}{A}$

18 x = 2(18)

By compairing

x= 2

The dimension of a physical quantity is constant.

The dimension of resistivity is $\mathbf { [ML^2T^{-2}A^{-2}]}$