Question

Find the equivalent resistance of the circuits shown in figure (32-E17)between the points a and b. Each resistor has a resistance r.

Figure 32-E17

Answer 1

(a) $R_{eff}=\frac{r\times r}{2r}=\frac{r}{2}\Omega$

(b) At O current coming to the junction is current going from BO = current going along OE

Current on CO = current on OD.

Thus, it can be assumed that current coming in OC goes in OB.

Thus, $[[r+(\frac{2r^2}{3r}+r)]=2r+\left(\frac{2r}{3}\right)=\frac{8}{3}]$

$R_{eff}=\frac{\frac{8r}{6}\times 2r}{\frac{8r}{6}+2r}$

$=8r^2\times \frac{2}{20r}=\frac{8r}{10}=\frac{4r}{5}$