Question

A uniform wire of resistence 15 ohm is bent to form a circle. The effective resistence between point X and Y is

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Answer 1

As we know

R = ρ l /A

As (ρ) is constant

And even A is constant because is it the same wire

So, R1/l1 = R2/l2

R1/R2 = l1/l2

If 2 pi is related to 360 *

2 pi /360 is related to 1*

So 2 pi /360 x 72 related to 72*

15/R2 = 2 pi x 360 / 2 pi x 72

15/R2 = 360/72

15/R2 = 5

R2 = 15/5 = 3 ohm

Answer 2

Answer:

The effective/equivalent resistance between $XY$ is $2.4$ $ohm$. The correct option is $2.4$ $ohm$.

Explanation:

• When the resistors are connected in a parallel combination, the net resistance is less than the resistance of each individual resistor.
• When we reduce the length of the conducting wire, the resistance of the wire also gets reduced.

Equivalent resistance in parallel combination:

$\frac{1}{R_{eq} } =\frac{1}{R_{1} } +\frac{1}{R_{2} }$

where $R_{eq$ is the equivalent resistance

            $R_{1},R_{2$  are the resistances.

Step 1:

The wire is bent in form of a circle.

So, the resistance of the minor arc $XY$ $=\frac{(72^{0} *15)}{360^{0} }$ $ohm$

                                                                 $= 3$ $ohm$

The resistance of the major arc $XY$ $= \frac{(288^{0} *15)}{360^{0} }$ $ohm$

                                                            $=12$ $ohm$

Step 2:

These two major and minor arcs wires $XY$ are connected in parallel.

So, between points $X$ and $Y$ effective resistance $=\frac{(12*3)}{(12+3)}$ $ohm$

                                                                                  $=2.4$ $ohm$

Hence, between points $X$ and $Y$ effective resistance is $2.4$ $ohm$.

The correct option is $2.4$ $ohm$.