If the two variables you know are across from one another, then multiplying them will get
you the third. If the two variables you know are above and below one another, then you
can get the third variable by dividing the one above by the one below. For instance, if you
know the power and the voltage in a given circuit, you can calculate the current by
dividing the power by the voltage.
Power and Resistance
We can combine the equations for power and Ohm’s Law to get expressions for power in
terms of resistance:
Heat
As current flows through a resistor, the resistor heats up. The heat in joules is given by:
where t is the time in seconds. In other words, a resistor heats up more when there is a
high current running through a strong resistor over a long stretch of time.
EXAMPLE
A circuit with a potential difference of 10 V is hooked up to a light bulb whose resistance is
20. The filament in the light bulb heats up, producing light. If the light bulb is left on for
one minute, how much heat is produced?We are being asked for the amount of heat that is dissipated, which is the product of
power and time. We have learned to express power in terms of voltage and resistance in
the formula P = V^2 /R. Applying that formula to the problem at hand, we find:
Then, plugging the appropriate numbers into the equation for heat, we find:
Every minute, the filament produces 300 J of heat.
Kilowatt-Hours
When electric companies determine how much to charge their clients, they measure the
power output and the amount of time in which this power was generated. Watts and
seconds are relatively small units, so they measure in kilowatt-hours, where one kilowatt
is equal to 1000 watts. Note that the kilowatt-hour, as a measure of power multiplied by
time, is a unit of energy. A quick calculation shows that: