# Question Video: Finding the Total Energy Output of a Device from the Useful Energy Output and Efficiency Physics

An LED light has an efficiency of 29%. If it converts 5,800 J to light, what is the total energy it was supplied with?

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### Video Transcript

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.