Question Video: Finding the Efficiency of a Device given Its Useful Power Output and Its Total Power Output Physics

A 120 W television has a useful power output of 30 W. What is the efficiency of the television?

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Video Transcript

A 120-watt television has a useful power output of 30 watts. What is the efficiency of the television?

Okay, so we have this television, and the television is rated at 120 watts. That means if we were to monitor the power coming into this television during its normal operation, that power would be at 120 watts. So that’s the total power input. And we’re told that this television has a useful power output of 30 watts. That is, the power that it uses in support of creating a moving image is 30 watts. So that leaves 90 watts doing something other than what we want them to be doing. Most of that wasted power goes into generating heat in the system. So then our television usefully outputs some of the power input to it but not all of it. And we want to calculate its efficiency.

Efficiency can be represented using the Greek letter 𝜂. It’s equal to the useful output from a process or a device divided by the total input. These outputs and inputs can be energies or, like in our case, they can be powers. In this instance, we’re told that the useful power output from this television is 30 watts and that the total power input is 120 watts. We can see when we calculate this fraction that the units, watts, will cancel out. And we’re left with 30 divided by 120. Written as a decimal, this is equal to 0.25.

Often though, efficiencies are expressed as percents. To write 0.25 as its equivalent value as a percent, all we need to do is multiply it by 100 percent. 0.25 times 100 percent is equal to 25 percent. That’s the efficiency of this television. It means that 25 percent of the total power input to it is converted to useful power output.

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