Question

40) A wire of resistanceroof 4w is bent in form of a circle.Find the equivalent resistance across
It's diameter.​

Answer 1

QUESTION  :-

A wire of resistance 4 ohm is bent in the form of a circle . Find the equivalent resistance across its diameter .

SOLUTION  :-

Resistance of the wire = 4 ohm

according to the question ,

the wire is bent in the form of a circle .

Now,

we have to find the equivalent resistance across its diameter

The resistance of one half of the circle would be equal to 2 ohm and the other part would also be 2 ohm.

both the 2 ohm resistances are in parallel combination.

In parallel combination,

equivalent resistance ( R eq )

1 / R eq =  1 / R₁  + 1 / R₂

here,

R₁  =  2 ohm

 R₂  = 2 ohm

now, putting the values in the above formula

    1 / R eq =  1 / 2Ω  +  1 / 2Ω

⇒   1 / R eq = ( 1+1) / 2Ω

⇒   1 / R eq  = 2 / 2Ω

⇒   R eq = 1 Ω

Therefore,

The equivalent resistance across its diameter is 1 ohm.