12.1 The Basic Electric Circuit

A basic electric circuit consists of four kinds of circuit elements, as follows.

1. A power source: This is a device for causing current to flow in the circuit. we will assume that this device produces a difference of potential across itself of where V and are constants.

2. A condenser or capacitor: This is like a small cut in the circuit, that current cannot cross. Current will flow in the rest of the circuit causing charge to build up on either side of the cut. The difference of potential across the cut will be proportional to the amount of charge that has built up, call it q, on the sides, and will be inversely proportional to the "capacity"of the cut to hold charge, which we denote as C thus to .

3. A coil or inductance. Faraday's law of inductance says that a changing current produces a difference of potential around a circuit. If you make a coil consisting of lots of windings of wire, you can observe this effect. If the current flow in the wires is i, then there will be a difference of potential caused by this effect that is proportional to and to the strength of the inductance which we denote by the letter L, hence to .

4. When current flows through a circuit, it hits obstacles which produce "resistance" which is, to a first approximation proportional to the current itself. This is described by the famous Ohm's Law: the difference in potential caused by this resistance is Ri where R is called the resistance of the circuit.

If we put all of this together, we find the equation

which states that the difference in potential across the circuit produced by the power source is the sum of the differences caused by the inductance capacity and resistance of the circuit.

If we add the fact that the current i in the circuit is the derivative of the charge q that builds up on the capacitor, this equation reads

which, apart from garbling the names of the constants (here V, , R, , and L), and of the variables, is exactly the same equation that we had with the forced and damped spring.

The phenomena associated with this circuit are in fact exactly like those we mentioned in the last section.