Question #4dd5f

1 Answer
Nov 6, 2016

the ans. will be 1 ohm.

Explanation:

we know R=s(l/a).where s=specific resistance of the element, l=length of the element,a=circular base area of the element.
now for the first case if resistance was R_1 and for the second case resistance will be R_2.
so R_1=s(l_1/a_1) and R_2=s(l_2/a_2)
now the diameter of the element is doubled ,so the radius of the circular base is also doubled.since, area=pi r^2,the area will be 4times.so,a_2=4a_1.
here the volume of the element will remain constant,so the product of the area & length remains the same i.e. a_1l_1=a_2l_2
again a_2=4a_1 hence l_2=l_1/4 .
since the element remains same s will be same for both the cases.

nowR_2=s(l_2/a_2)=s((l_1/4)/(4a_1))=s(l_1/(16a_1))=R_1/16=16/16=1 ohm.