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:
