Voltage, Current, and Resistance

The state of an ideal resistor is completely specified by the voltage across it (call it $V$ volts) and the current passing through it ($I$ amperes, or simply ``amps''). The ratio of voltage to current gives the value of the resistor ($V/I = R =$ resistance in Ohms). The fundamental relation between voltage and current in a resistor is called Ohm's Law:

$$V(t) = R \cdot I(t)$$   (Ohm's Law)

where we have indicated also that the voltage and current may vary with time (while the resistor value normally does not).

The electrical power in watts dissipated by a resistor R is given by

$${\cal P}= V\cdot I = \frac{V^2}{R} = R\cdot I^2$$

where $V$ is the voltage and $I$ is the current. Thus, volts times amps gives watts. Also, volts squared over ohms equals watts, and so on.