
Prerequisites :
Differential Equations of First Order and First Degree
Linear Differential Equations of Higher Order
There are 3 basic components of an electric circuit, where a change in voltage is possible. They are:
1) Resistance (), voltage drop = , we saw this in Ohm’s law.
2) Capacitance (), voltage drop =
3) Inductance (), voltage drop =
Note that the electric current is the rate of flow of charge , hence, .
To solve a differential equation, we use the Kirchoff’s voltage law, which states that the sum of all the voltages around a loop is equal to zero.
The general circuit will consist of all 3 elements, and as well as the voltage source, . The D.E. will be
Expressing in terms of the amount of charge, ,
is the frequency of applied voltage.
Resonance is a special condition in circuits, when the imaginary parts of impedances due to inductor and capacitor cancel each other. It occurs when the applied frequency becomes equal to the natural frequency, given by