Question

Apply the loop rule to loop abcdefghija in Figure 21.52.

Short answer

The loop rule to loop abcdefghija is:

$-{\mathrm{I}}_2{\mathrm{R}}_2+{\mathrm{E}}_1-{\mathrm{r}}_1{\mathrm{I}}_1-{\mathrm{R}}_5{\mathrm{I}}_1-{\mathrm{r}}_4{\mathrm{I}}_3-{\mathrm{E}}_4-{\mathrm{r}}_3{\mathrm{I}}_3+{\mathrm{E}}_3+{\mathrm{R}}_3{\mathrm{I}}_3=0$

Step-by-step solution

Definition of Kirchhoff's law

Kirchhoff's first law defines currents at circuit junctions. It states that the sum of currents flowing into and out of a junction in an electrical circuit equals the sum of currents flowing out of the junction.

Explanation for the loop abcdefghija

An equation for loop abcdefghija in the Figure 21.52 can be found by applying the loop rule:

$-{\mathrm{I}}_2{\mathrm{R}}_2+{\mathrm{E}}_1-{\mathrm{r}}_1{\mathrm{I}}_1-{\mathrm{R}}_5{\mathrm{I}}_1-{\mathrm{r}}_4{\mathrm{I}}_3-{\mathrm{E}}_4-{\mathrm{r}}_3{\mathrm{I}}_3+{\mathrm{E}}_3+{\mathrm{R}}_3{\mathrm{I}}_3=0$

Sources acting in the same direction as the current flow are declared positive, whereas resistances and sources acting in the opposite direction are declared negative.

Therefore,the loop for abcdefghija is:

$-{\mathrm{I}}_2{\mathrm{R}}_2+{\mathrm{E}}_1-{\mathrm{r}}_1{\mathrm{I}}_1-{\mathrm{R}}_5{\mathrm{I}}_1-{\mathrm{r}}_4{\mathrm{I}}_3-{\mathrm{E}}_4-{\mathrm{r}}_3{\mathrm{I}}_3+{\mathrm{E}}_3+{\mathrm{R}}_3{\mathrm{I}}_3=0$