Question

A wire of resistance 2R is bent in the form of a circle. what is the effective resistance between the ends of the diameter.

Answer 1

Answer:

Explanation:

if we bent sire in a circular form ,

then

length of wire = perimeter of circle

let length of wire is L

then ,

L = π× diameter of circle

diameter = L/π

now , semiperimer of circle =π/2× diameter = L/2

we know,

resitance depends upon length and cross sectional area of wire .

e.g R = pl/A

where p is resistivity .

but here only length change e.g half so,

resistance exist in two semiperimeter is half e.g 2R

now ,

let A and B is the end of diameter then combination of both above and below , wire is In parallel combination .

so, effective resistance = Req

1/Req = 1/R1 + 1/R2

= 1/2R + 1/2R

= 1/R

Req = R