Question

A wire of resistance r is bent in the form of a circle .the resistance between two points on the circumference of the wire and at the cnd of a diameter of the circle is

Answer 1

Final Answer :
$\frac{\pi \times r}{2} ohm$


Steps and Understanding :
1) Since, Diameter divides the circle in two equal parts .
So, each part is of ( πr) ohm. 

2) Both are Parallel along a diameter. 
So, Effective Resistance
$\frac{1}{z} = \frac{1}{\pi \times \: r } + \frac{1}{\pi \times r} \\ \\ = > \frac{1}{z} = \frac{2}{\pi \times r} \\ \\ = > z = \frac{\pi \times r}{2 } \\ \\ = > z = \frac{\pi \times r}{2}$

So, Effective Resistance between ends of a diameter is( π *r/2 )ohm.

Answer 2

Thank you for asking this question, the options for this question are missing:

Here are the missing options:

A) Rα4π2(2π−α)

B) R2π(2π−α)

C) R(2p  a)

D)  4πRα(2π−α)

Answer:

The correct answer for this question is Option A: Rα4π2(2π−α)

RXWY=R/2πr×(rα)=Rα/2π  

(∵α=l/r)

and  

RXZY=R/2πr×r(2π−α)

=R/2π(2π−α) Req

=RXWYRXZY/RXWY+RXZY

=Rα/2π×R/2π(2π−α)/Rα/2π+R(2π−α)/2π

=Rα/4π2(2π−α)

If there is any confusion please leave a comment below.