Calculate the effective resistances between the points `A and B` in the networks shown in (Fig. 3.20)
(a) and (Fig. 3.20)(b).
.

Answer

(a) `1 Omega`
(b) `0.71 Omega`

Explanation

In (fig. 3.25)(a), `1 Omega and 2 Omega` are in series and their resultant resistance is `3 Omega`. Now `3 Omega and 1.5 Omega` are in parallel and their equivalent resistance `=(3 xx 1.5)/(3 + 1.5) Omega = 1 Omega`
In (Fig. 3.25)(b), resistance in the arm CD, i.e., `r_1 = 5 Omega` , resistance in the arm `ADB`, i.e., `R_2 = 5 Omega`. Now, `R_1, 1 Omega and R_2` are in parallel.
If `R` is their equivalent resistance, `(1)/( R)=(1)/(R_1)+(1)/(1)+(1)/(R_2)=(1)/(5)+(1)/(1)+(1)/(5)=(7)/(5)` or `R = (5)/(7) Omega = 0.71 Omega`.