Chapter 4.6, Problem 15E

(a)

To determine

To show: The system of differential equation for the currents $i_2\left(t\right)$ and $i_3\left(t\right)$ in the electrical network is $L_1\frac{d{i}_2}{dt}+R{i}_2+R{i}_3=E\left(t\right)$ and $L_2\frac{d{i}_3}{dt}+R{i}_2+R{i}_3=E\left(t\right)$ using Laplace transformation.

(b)

To determine

The system of differential equation $L_1\frac{d{i}_2}{dt}+R{i}_2+R{i}_3=E\left(t\right)$ and $L_2\frac{d{i}_3}{dt}+R{i}_2+R{i}_3=E\left(t\right)$ for the currents $i_2\left(t\right)$ and $i_3\left(t\right)$ in the electrical network if $R=5\Omega ,L_1=0.01\text{h},L_2=0.0125\text{h},E=100\text{V}$ and $i_2\left(0\right)=0,i_3\left(0\right)=0$ using Laplace transformation.

(c)

To determine

The expression for current $i_1\left(t\right)$ using Laplace transformation.