Question

Please Answer this question

A piece of wire of resistance r is cut into two equal parts. If this two parts are now connected in parallel, then state how the resistance and the resistivity of the combination will change. Justify your answer

Answer 1

Answer ⇒  Resistivity remains unchanged and resistice of combination is r/4.

Explanation ⇒ Resistivity being an property of the matter do not changes either its length or area of cross section changes.

Now, As per as the question, A wire having Resistance 'r' is break into 2 equal parts,

then, Resistance will becomes half. You know how, Let us check.

Let length of wire be L. After it is break, then length of each parts be L/2.

Area will remains same, since it is nor stretched or compressed, but breaken from middle.

Resistivity will remains unchanged.

Thus, Resistivity Initial = Resistivity final.

rA/L = RA/(L/2)

r = 2R

OR R = r/2

This means Resistance will becomes half.

When the are connected in parallel, then Equivalent resistance is given by the expression,

Re = r/4

Hence, the Resistance of the combination will be r/4 and its resistivity of combination initially and finally will be always same.

Hope it helps.

Answer 2

Let the starting resistance is R, now cut it half into two pieces now two resistance is R/2 and R/2 right

now come to the parallel combination

1/Req=1/r1+1/r2

there for.1/(r/2)+1/(r/2)

It will look like.2/R+2/R=4/R

Now R equivalent=R/4 so answer will be R/4❤️