Question #4dd5f

1 Answer
Rajat Chatterjee
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.

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#.

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