A wire 7ohm/metre is turned in the form of a circle of the diameter 2metre.Find the resistance across the ends of the diameter.
Answers
Here, the wire is in the form of a circle , with the upper part and lower part forming a semicircle .
As, circumference of semicircle = pi * r
So, the length of upper part = pi * r
= (22/7) * 1
= 22/7 m
the length of below part = pi * r
= (22/7) * 1
= 22/7 m
So, the resistance of upper part = (7ohm/metre) * (22/7 metre)
= 22 ohm
the resistance of below part = (7ohm/metre) * (22/7 metre)
= 22 ohm
These two resistances upper and below part are in parallel with each other.
So, resistance across the ends of the diameter = Req
=> 1/Req = 1/Rupper + 1/Rlower
=> 1/Req = 1/22 + 1/22
=> 1/Req = 2/22
= 1/11
=> Req = 11 ohm
Thus, the resistance across the ends of the diameter = 11 ohm