11. Consider an electric circuit like that in Example 5 of Section 8.6. Assume the electromotive force is an alternating current generator which produces a voltage V(t) = E sinwt , where E and w are positive constants (w is the Greek letter omega).
EXAMPLE 5. Electric Circuits. Figure 8.2(a), page 318, shows an electric circuit which has an electromotive force, a resistor, and an inductor connected in series. The electromotive forces produces a voltage which causes an electric current to flow in the
circuit. If the reader is not familiar with electric circuits, he should not be concerned. For our purposes, all we need to know about the circuit is that the voltage, denoted by V(t), and the current, denoted by I(t), are functions of time t related by a differential equation of the form
LI '(t ) + RI(t ) =V(t )
Here L and R are assumed to be positive constants. They are called respectively, the inductance and resistance of the circuit.
Please see attached file for full problem description.
Please see the attached file.
This is a typical problem of solving a first order non-homogeneous differential equation. We have:
with L and R being constants.
There are good references which relate to solving these equations.
Good for explaining homogeneous ...
The solution provides a theoretical explanation and then a very detailed and step-by-step work-out for the problem.