Four resistances of 2.0 `Omega` each are joined end to end, to form a square ABCD. Calculate the equivalent resistance of the combination between any two adjacent corners

Explanation

Fig. shows four resistors each of resistance 2.0 `Omega ` joined end to end to form a square ABCD. We are to find the equivalent resistance of the combination between the adjacent corners A and B.

Between A and B, there are three resistors in the arms AD, DC and CB in series in one branch. The equivalent resistance of this branch is `R_s = 2.0 + 2.0 + 2.0 = 6.0 Omega `. Now one resistor `(= 2:0 Omega )` in arm AB is in parallel combination with the equivalent resistance `R_s (= 6 Omega )` as shown in Fig.

If the equivalent resistance between the points A and B in Fig is ` R_P` then
` (1)/(R_p) = 1/6 + 1/2 = (1+3)/(6) = 4/6`
or ` R_p = 6/4 = 1.5 Omega`