Question

a wire of resistance 20 ohm is streched upto double of its length .find its new resistance

Answer 1

Resistance is directly proporsional to length

Ans is 40 ohms

Answer 2

R=( p*l)/A

P(rho)= resistivity of material

L= length

A= area of cross section

Now volume of the conductor will not change when you elongate it.

A(1)* l(1)= A(2) * l(2). Now we have l(2)= 2l(1). So we get A(2)= A(1)/2. So when you elongate the length the cross section of the conductor decreases .

R(2) = p * l(2)/ A(2) rho is independent of geometry of conductor.

R(2) = ( p* 2l(1)) / ((A(1)/2) )

R(2)= 4 ( p * l(1))/( A(1) )

= 4 * 20= 80 ohms

So change is 80–20= 60ohms.

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