Question

Question #4dd5f

Answer 1

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.

now`R_2=s(l_2/a_2)`=`s((l_1/4)/(4a_1))`=`s(l_1/(16a_1))`=`R_1/16`=`16/16`=`1 ohm`.