Find the equivalent resistance between points | vedclass

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(D) In the given circuit,point $A$ is the center of the circle. Four resistors,each of resistance $r$,are connected between the center $A$ and four po

Vedclass · Accepted Answer

$\frac{r}{4}$

Vedclass · Answer

(D) In the given circuit,point $A$ is the center of the circle. Four resistors,each of resistance $r$,are connected between the center $A$ and four points on the circumference $(B, C, D, E)$.When we look at the circuit from the perspective of points $A$ and $B$,we can see that all four resistors are connected in parallel between point $A$ and the outer ring (which effectively acts as a single node for the other ends of the resistors).Since all four resistors of resistance $r$ are connected in parallel,the equivalent resistance $R_{AB}$ is given by the formula:$\frac{1}{R_{AB}} = \frac{1}{r} + \frac{1}{r} + \frac{1}{r} + \frac{1}{r}$$\frac{1}{R_{AB}} = \frac{4}{r}$Therefore,$R_{AB} = \frac{r}{4}$.

Find the equivalent resistance between points $A$ and $B$.

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