Differential Equation Applications

Kirchoff’s Law

The current, i in a series circuit with constant inductance, L , constant resistance, R and a constant voltage, V applied is described by:

L di/dt + Ri = V

If we have such a circuit with L = 3 henrys, R = 8 ohms, V = 20 volts, find the current after 60 seconds.

What is known?

This is a nice problem, because the equation is given, we need only to plug in the given values:

3 di/dt + 8i = 20

We are looking for i = ? when t = 60.

Separate variables and integrate:

3 di/(20-8i) = dt

Integrating: -3ln(20-8i)/8 = t + C

Now, solve for the constants: