Question

A uniform wire of resistance 15 Q is bent to form a circle. The effective resistance between point X and Y is​

Answer 1

Answer:

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Answer 2

Answer:

Explanation:

Concept:

The resistance between two sites in any electric network or electric circuit is referred to as effective resistance. The effective resistance of any electric circuit where there are two or more resistors is equal to the sum of all the resistors employed in that circuit. Both series and parallel circuits can have differing effective resistances.
Given:

A uniform wire of resistance 15 ohm  is bent to form a circle
Find:

The effective resistance between point X and Y is​
Solution:

The net resistance, which results from connecting the resistors in parallel, is lower than the resistance of each individual resistor.

The resistance of the conducting wire similarly decreases when its length is decreased.

Equivalent resistance in parallel combination:

      $\frac{1}{R_{e q}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$

Where $R_{e q}$ is the equivalent resistance $R_{1}, R_{2}$ are the resistances.

Step 1:

The wire is curved into a circular.

As a result, the minor arc's resistance $X Y=\frac{\left(72^{0} * 15\right)}{360^{0}}$ ohm

$= 3 \text { ohm }$

The major arc's resistance  $X Y=\frac{\left(288^{0} * 15\right)}{360^{0}}}$ ohm

$= 12 \mathrm{ohm}$

Step 2:

These two major and minor arcs wires X Y are connected in parallel. So, between points X and Y effective resistance $=\frac{(12 * 3)}{(12+3)} \mathrm{ohm}$

$= 2.4 \mathrm{ohm}$

Hence, between points X and Y effective resistance is $2.4 \ \mathrm{ohm}$.

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