Theory of Circuits

Everything electrical begins with a single property of matter, charge, that comes in two kinds, is never created or destroyed, and pushes on other charge through a field that fills the space around it.

Voltage is electric potential energy per unit charge, the electrical height that a source lifts charge to, and a difference in it is the only thing that makes charge flow.

Current is the rate at which charge passes a point, measured in amperes, and although the individual charges drift astonishingly slowly, the push that starts them moving travels almost instantly.

Resistance measures how strongly a material opposes current, and for most materials the current is simply proportional to the voltage across them, the single most used relation in the whole subject.

Power is voltage times current, the rate at which a component turns electrical energy into heat, light or motion, and combining it with Ohm's law explains why current, not voltage, is what melts a wire.

Two conservation laws, one for the charge at every junction and one for the energy around every loop, combine with Ohm's law to reduce any network of resistors to a single number.

When a circuit will not collapse into series and parallel groups, labelling the voltage at each node and writing the current balance there solves it, and any two-terminal network can be replaced by a single source and resistor.

Two conductors held close store charge in proportion to the voltage across them, keeping energy in the electric field between them, and they pass changing signals while blocking steady ones.

A resistor charging a capacitor makes the voltage climb along an exponential curve whose whole pace is set by one number, the product of the resistance and the capacitance.

A current makes a magnetic field, a coil concentrates it, and the field's reluctance to change gives the inductor a behaviour that mirrors the capacitor at every turn: it resists changes in current the way a capacitor resists changes in voltage.

The electricity from a wall socket does not flow one way but swings back and forth as a sine wave, chosen because it is easy to generate and to transform, and its useful value is not its peak but the steady value that would heat a resistor equally.

In alternating current a capacitor and an inductor oppose the flow in a way that depends on frequency and shifts the timing, and when their opposite effects cancel at one special frequency the circuit rings, which is how a radio picks one station from the air.