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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:

$\displaystyle V(t) = R \cdot I(t)$   (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

$\displaystyle {\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.

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