Laplace transforms: Circuit

Part 1:

Problem Statment. Solve the circuit using Laplace transforms.

Solution:

By Kirchoff's First Law i1=i2+i3. applying Kirchoffs second law we get:

E(t)R(i1)+L1(I2)' using the first law this can be written as

E(t)=L1(i2)'+R(i2)+R(i3) E(t)=L1(i3)'+R(i2)+R(i3)

In differential form the system is written as: