91Ó°ÊÓ

We need to find the equivalent resistance between points a and b.

The resistors are connected one by one and with no junctions between them then they are called to be connected in series. For a series resistors, the equivalent resistance for their combination is given by equation in the form

$R_{eq}=R_1+R_2+....+ R_N$ (1)

In figure EX28.28, there are three resistors , and are connected in series, so let us find the equivalent resistance for this combination using equation (1) by

$R_{1,eq}=100\mathrm{Î\copyright }+ 100\mathrm{Î\copyright }+100\mathrm{Î\copyright }=300\mathrm{Î\copyright }$

Also, there are two resistors that are connected in series. Calculating the equivalent resistance for this combination using equation (1) by

$R_{2,eq}=100\mathrm{Î\copyright }+ 100\mathrm{Î\copyright }=200\mathrm{Î\copyright }$

Between the two points a and b, the two combinations $R_{2,eq}$and $R_{1,eq}$are connected in parallel with each other and with the resistance $100\mathrm{Î\copyright }$. The equation shows the equivalent resistance for the parallel connection in the form

$\frac{1}{R_{eq}}=\frac{1}{R_1}+ \frac{1}{R_2}+ ....+ \frac{1}{R_N}$ (2)

We use the values for $R_{2,eq,}{R}_{1,eq}$, and $100\mathrm{Î\copyright }$into equation (2) to get the equivalent resistance between points a and b by

$$\begin{gathered} \frac{1}{R_{ab}}=\frac{1}{R_{1,eq}}+\frac{1}{R_{2,eq}}+\frac{1}{100\mathrm{Î\copyright }} \\ \frac{1}{R_{ab}}=\frac{1}{200\mathrm{Î\copyright }}+\frac{1}{300\mathrm{Î\copyright }}+\frac{1}{100\mathrm{Î\copyright }} \\ {R}_{ab}={\left(\frac{1}{200\mathrm{Î\copyright }}+\frac{1}{300\mathrm{Î\copyright }}+\frac{1}{100\mathrm{Î\copyright }}\right)}^{-1} \\ {R}_{ab}=54.5\mathrm{Î\copyright } \end{gathered}$$