Question

what is the equivalent resistance of the network between points A and B is Resistance is of the value r

Answer 1

4/r if we take parallel connection between A and B

Answer 2

Answer:

Equivalent resistance = $\dfrac{r}{4}$

Explanation:

Assume:

R = equivalent resistance between the points A and B

If we imagine to stretch the points A and B apart and redraw it, we see that the circuit is a parallel combination of four similar resistors having resistance r each.

We also know that the following relation will be used to calculate the equivalent resistance between these two points.

$\dfrac{1}{R}=\dfrac{1}{r}+\dfrac{1}{r}+\dfrac{1}{r}+\dfrac{1}{r}\\\Rightrarrow \dfrac{1}{R}=\dfrac{4}{r}\\\Rightrarrow R = \dfrac{r}{4}$

Hence, the equivalent resistance between the points A and B is $\dfrac{r}{4}$.