Question

A uniform wire of resistance 4 ohms is bent into the form of a circle of radius R. A specimen of the same wire is connected along the diameter of the circle. What is the equivalent resistance across the ends of the wire?

Answer 1

Let the resistance per unit length be \lambda. Then,

\lambda = 4/2\pi r

=> resistance of the specimen wire connected along the diameter is:

R = \lambda \times 2r = \frac{4}{\pi } \Omega

Now after the specimen wire is connected along the diameter, three resistance come in parallel:

2 \Omega (resistance of one half of the circumference), 2 \Omega (resistance of the other half of the circumference) and R(resistance of the diameter). Solving, we get:

{\color{DarkRed}R_{eq} = \frac{4}{4+\pi } \Omega }

Answer 2

Answer:

ExplanaTION = RESISTANCE BETWEEN AB WILL COME 4/4+PI OHM