Question

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

Answer 1

Explanation:

When a wire of resistance 4R is bent in the form of circle, then the resistance of each segment across the diameter becomes 2Ras shown in the figure.

Equivalent resistance between A and B: RAB1=R11+RB1            (in parallel combination)

∴   RAB1=2R1+2R1 

RAB1=2R2                  

⟹  RAB=R



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Answer 2

Resistance of wire = 4 ohm

Let length of the wire is 'a' units.

Thus, resistance per unit length = 4/a ohm

Let the radius of the circle formed is 'r'.

Thus, Circumference of Circle = Length of Wire

=> 2πr = a

r = a/2π

Now,

Resistance of the arc AOB = (Resistance per unit length) × (Length of arc AOB)

= 4/a × π(a/2π)

= 4/a × a/2

= 2 ohm

Similarly,

Resistance of arc AO'B = 2 ohm.

Also,

The arcs AOB and AO'B are connected in parallel connection.

Thus,

Resistance across diameter (Req) is:

1/(Req) = 1/2 + 1/2

= 2/2

= 1 ohm.

Hence, the resistance across the diametrically opposite points is 1 ohm.