Question

uniform wire of resistance R ohm is bent into a circular loop.Compute the effective resistance between the diagrammatically opposite points A and B

Answer 1

Concept Introduction:-

It could take the shape of a word or a numerical representation of a quantity's arithmetic value.

Given Information:-

We have been given that uniform wire of resistance R ohm is bent into a circular loop.

To Find:-

We have to find that Compute the effective resistance between the diagrammatically opposite points A and B

Solution:-

According to the problem

Draw resistance structure [Ref. Fig.]

Resistance of both part will be $R / 2$ because wire is uniform.

Equivalent resistance between $A$ and $B$,

Each resistor has both terminals connected to both terminals of the others so both are in parallel-

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

$\Rightarrow R_{A B}=\frac{\frac{R}{2} \times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{R}{4}$

Final Answer:-

Equivalent resistance between any two of diametrically opposite points will be $\frac{R}{4}$.

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