An LED light has an efficiency of
29 percent. If it converts 5,800 joules to
light, what is the total energy it was supplied with?
Okay, so we have an LED light. And that light has a given
efficiency. This LED is supplied with some
total amount of energy. And then it outputs a given amount
of energy as light. And that given amount, we’re told,
is 5800 joules. We can consider this to be useful
output energy from the LED. And this useful energy output is
some fraction of the total energy input into the device. Now, if our LED was perfectly
efficient, then all of the energy we input to it would be converted to useful energy
output as light.
But we know that that’s not the
case. Rather, just under 30 percent of
the input energy is converted into useful output energy. That’s what it means that the
efficiency of this LED is 29 percent. So basically, we input some total
amount of energy to our LED and then 29 percent of that total input is output as the
5800 joules of light energy. And knowing this, we want to work
backward to solve for that total energy input.
Let’s let the total energy supplied
to our LED be represented by this symbol, 𝐸 sub t. And then let’s let 𝐸 sub L
represent the energy that our LED converted to light. The LED efficiency of 29 percent
means that if we take 29 percent of 𝐸 sub t, then that will equal 𝐸 sub L. Written out using words, 29 percent
of 𝐸 sub t equals 𝐸 sub L. And now, we can translate this into
an equation that we can solve for 𝐸 sub t. To do that, we’ll want to convert
this percent, 29 percent, into a decimal. In general, if we have a number
written as a percent — we’ll call it 𝑁 sub P — then if we divide that value by 100
percent, that equals the equivalent number written as a decimal.
So if we take 29 percent and divide
that by 100 percent, we see the percent signs cancel out. And as a decimal, this fraction is
equal to 0.29. So if we take this number, 0.29,
and multiply it by 𝐸 sub t, the total energy supplied to the LED, then that product
will equal 𝐸 sub L, the energy output as light. Written as an equation, we can say
that 0.29 times 𝐸 sub t equals 𝐸 sub L. And to solve for 𝐸 sub t, the
total energy, we’ll divide both sides of the equation by 0.29. That will cancel that term out on
the left. And we see that the total energy
input is equal to the light energy, the useful energy output, divided by 0.29.
And we know 𝐸 sub L, the energy
converted to light; that’s 5800 joules. So 𝐸 sub t is 5800 joules divided
by 0.29 which is equal to 20000 joules. That’s the total energy supplied to
this LED light.