## 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.