Question

A wire has resistance $12\Omega$. It is bent in the form of a circle. The effective resistance between the two points on any diameter is equal to

• A. $12\Omega$
• B. $6\Omega$
• C. $3\Omega$
• D. $24\Omega$

Answer 1

Answer: (C)

Step 1: Given that:

The resistance of wire = 12Ω

It is bent in the form of a circle.

Step 2: Calculation of the effective resistance between the two points on any diameter:

As the wire is bent in the form of a circle and the diameter divides a circle into two halves,

The resistance of the two parts will be equal.

That is;

The resistance of the part ACB = Resistance of the part ADB

Since, The resistance of the whole wire = 12Ω

Resistance of each equal part = $\frac{\text{12Ω}}{2}$ = 6Ω

Now,

Both the parts are connected in parallel, therefore the effective resistance between diameter AB will be given as;

$\frac{1}{R_{eff}}=\frac{1}{6\Omega }+\frac{1}{6\Omega }$

$\frac{1}{R_{eff}}=\frac{2}{6}$

$\frac{1}{R_{eff}}=\frac{1}{3}$

$R_{eff}=3\Omega$

Thus,

The effective resistance along any diameter will be $3\Omega$ .

Thus,

Option D) $3\Omega$ is the correct option.