Question

A uniform wire of resistance 27 ohm is bent to form a circle. The effective resistance between two points separated by 60 degree is

Answer 1

Answer:

6 ohm is the correct answer.

Explanation:

Given data:

A uniform wire is bent to form a circle.

resistance = 27 ohm

To find:

effective resistance between two points separated by 60 degree =?

Solution

When the wire is bent into a circle the resistances are connected in parallel.

Let us consider L as the length of wire.

A circle has angle 360° and it uses complete length of wire L.

Resistance per unit length of wire is given by = 36/L

This for 1 degree the length of wire used will be L/360.

Now for given data that is 60°

The length L will be = L*60/360

=L/6

Thus

The resistance of circular wire will be given by

=(L/6) * (36/L)

=6 ohm

Hence, 6 ohm is the correct answer.

Answer 2

Answer:

1 degree = 18/360 ohms

the circle is in parallel connection

let the major arc be r1 and minor arc r2

resistence of wire is 18 ohms

r1= 18x300 degrees/ 360 = 15ohms

r2= 18x60 degrees /360 =3 ohms

since the connection is in parallel

1/r1 + 1/r2 = 1/ Req

1/15+1/3= 15/6 ohms

i hope u got urs ans :)