Question

If the area of cross section of a resistance wire is halved , then its resistance becomes
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Answer 1

Answer:

Resistance becomes double

Explanation:

Because resistance is directly proportional to length and inversely proportional to the cross -section area of wire.

so,it becomes double.

Answer 2

Answer

• R' = 2R

Given

• The area of cross section of a resistance wire is halved

To Find

• New resistance

Formula Used

$\bullet \;\; \bf R=\dfrac{\rho l}{A}$

Solution

For a wire having resistivity , ρ , length , l , Area of cross-section , A and Resistivity , R is ,

$\bullet \;\; \rm R=\dfrac{\rho l}{A}...(1)$

If the area of cross-section is halved , new Area be A' ,

• A'  = A/2

And also , new resistance be R' .

$\implies \rm R'=\dfrac{\rho l}{(A')}\\\\\implies \rm R'=\dfrac{\rho l}{(\frac{A}{2})}\\\\\implies \rm R'=\dfrac{2 \rho l}{A}\\\\\implies \rm R'=2\bigg(\dfrac{\rho l}{A}\bigg)\\\\\implies \rm R'=2R\;\;[\; From\ (1)\;]$

So , new resistance will doubled the old