Question

a metal cube with side of lenth a has electrical resistance R between opposite faces what is the resistance between the opposite face of the same cube with side 3a length?​

Answer 1

The resistance will become 3 times

Explanation:

The resistance across a conductor can be found by the relation

R = ρ l/A

here ρ is the resistivity  of conductor

l is the length of conductor and A is its area of cross-section

In this case l = a  and A = a²

Therefore resistance R =  ρ x 1/a                I

Now if the conductor becomes 3 a on side .

Thus in this case l = 3 a

and A = 9 a²

This R₁ =  ρ 3a/9a² =  ρ x 1/3a                     II

Dividing II by I

R₁/R = 1/3

Thus R₁ = 3 R

Answer 2

Answer

R/3

Explanation

R=pL/A ..

When length is a and cross sectional area is a2.  R=pa/a^2 =1/a....(1)

WHEN length becomes 3a then cross sectional area becomes 3a×3a=9a^2 then new resistance becomes

R°=p3a/9a^2 =1/3a...... (2)

Now put value of R=1/a from.... (1) in.. (2)

R°=R/3

Hope it helps