91影视

In a series circuit, the current in each resistor is the same because the output current of the first resistor flows into the input of the second resistor.

In a parallel circuit, all of the resistor leads on one side are linked together, and all of the resistors leads on the other side are linked together.

Applying the junction rule for point a:

$$\begin{gathered} {\mathrm{I}}_1={\mathrm{I}}_2+{\mathrm{I}}_3 \\ {\mathrm{I}}_1鈥�{\mathrm{I}}_2鈥�{\mathrm{I}}_3=0 \end{gathered}$$鈥︹赌︹赌︹赌︹赌︹赌︹赌︹赌︹赌�(1)

Using Kirchoff's loop rule to the loop abcdefgha,

We have

$鈥�{\mathrm{I}}_2{\mathrm{R}}_2+{\mathrm{E}}_1鈥�{\mathrm{I}}_2{\mathrm{r}}_2+{\mathrm{I}}_3{\mathrm{R}}_3+{\mathrm{I}}_3{\mathrm{r}}_3鈥�{\mathrm{E}}_2=0$

Substituting the values, we have

$$\begin{gathered} 鈥�{\mathrm{I}}_2\left(2.5\mathrm{惟}\right)+18\mathrm{V}鈥�{\mathrm{I}}_2\left(0.5\mathrm{惟}\right)+{\mathrm{I}}_3\left(1.5\mathrm{惟}\right)+{\mathrm{I}}_3\left(0.5\mathrm{惟}\right)鈥�45\mathrm{V}=0 \\ 鈥�2{\mathrm{I}}_3鈥�3{\mathrm{I}}_2鈥�27=0 \end{gathered}$$鈥︹赌︹赌︹赌︹赌�.(2)

Again, applying Kirchoff's loop rule to the loop aefgha,

${\mathrm{I}}_2{\mathrm{R}}_1+{\mathrm{I}}_3{\mathrm{R}}_3+{\mathrm{I}}_3{\mathrm{r}}_2鈥�{\mathrm{E}}_2=0$

Substituting the values,

$$\begin{gathered} {\mathrm{I}}_1\left(6\mathrm{惟}\right)+{\mathrm{I}}_3\left(1.5\mathrm{惟}\right)+{\mathrm{I}}_3\left(0.5\mathrm{惟}\right)鈥�45\mathrm{V}=0 \\ 6{\mathrm{I}}_1+2{\mathrm{I}}_3鈥�45=0 \end{gathered}$$鈥︹赌︹赌︹赌︹赌︹赌︹赌︹赌︹赌�.(3)

By solving equations(1), (2), and (3), we have,

$$\begin{gathered} {\mathrm{I}}_1=4.75\mathrm{A} \\ {\mathrm{I}}_2=-3.50\mathrm{A} \\ {\mathrm{I}}_3=8.25\mathrm{A} \end{gathered}$$

Hence, the values of currents are:

$$\begin{gathered} {\mathrm{I}}_1=4.75\mathrm{A} \\ {\mathrm{I}}_2=-3.50\mathrm{A} \\ {\mathrm{I}}_3=8.25\mathrm{A} \end{gathered}$$