Calculating electric
power
We've seen the formula for determining the
power in an electric circuit: by multiplying the voltage in
"volts" by the current in "amps" we arrive at an answer in
"watts." Let's apply this to a circuit example:
In the above circuit, we know we have a
battery voltage of 18 volts and a lamp resistance of 3 Ω.
Using Ohm's Law to determine current, we get:
Now that we know the current, we can take
that value and multiply it by the voltage to determine
power:
Answer: the lamp is dissipating (releasing)
108 watts of power, most likely in the form of both light
and heat.
Let's try taking that same circuit and
increasing the battery voltage to see what happens.
Intuition should tell us that the circuit current will
increase as the voltage increases and the lamp resistance
stays the same. Likewise, the power will increase as well:
Now, the battery voltage is 36 volts instead
of 18 volts. The lamp is still providing 3 Ω of electrical
resistance to the flow of electrons. The current is now:
This stands to reason: if I = E/R, and we
double E while R stays the same, the current should double.
Indeed, it has: we now have 12 amps of current instead of 6.
Now, what about power?
Notice that the power has increased just as
we might have suspected, but it increased quite a bit more
than the current. Why is this? Because power is a function
of voltage multiplied by current, and both voltage
and current doubled from their previous values, the power
will increase by a factor of 2 x 2, or 4. You can check this
by dividing 432 watts by 108 watts and seeing that the ratio
between them is indeed 4.
Using algebra again to manipulate the
formulae, we can take our original power formula and modify
it for applications where we don't know both voltage and
resistance:
If we only know voltage (E) and resistance
(R):
If we only know current (I) and resistance
(R):
An historical note: it was James Prescott
Joule, not Georg Simon Ohm, who first discovered the
mathematical relationship between power dissipation and
current through a resistance. This discovery, published in
1841, followed the form of the last equation (P = I2R),
and is properly known as Joule's Law. However, these power
equations are so commonly associated with the Ohm's Law
equations relating voltage, current, and resistance (E=IR ;
I=E/R ; and R=E/I) that they are frequently credited to Ohm.
|
