You have a special light bulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?

Video transcript

Hi, everyone in this practice problem, we're being asked to determine the maximum root mean square or R MS current that can be safely passed through an extension cord. We'll have an extension cord used with a portable electric fan heater and the manufacturers warn against using the extension cords. However, if one must be used, they recommend the current should never exceed 3.2 amp. And we're being asked to determine the maximum R MS current that can be safely passed through to extension court. The options given are a 1.45 MB 4. AC 6.81 amp and lastly D 2.26 amp. So the maximum current is going to be the current amplitude. And from this problem statement, it is given that it must not ever exceed 3. amp or in this case, I or the current amplitude is going to be 3.2 amp. We know that the formula for Ir MS will then be equals to I divided by the square root of two. And now we can actually substitute our I value into this formula in order for us to get the R MS current or the root mean squared current. So let's start by doing that. So I will eat 3.2 amp divided by a squared of two, which will be equals to the IRM si is the current amplitude or the maximum value of the current. And calculating this, we will then get the Ir MS value to be 2. amp. Hence the current amplitude is going to be larger than the root mean squared current where the Ir MS is just going to be 2.26 amp, which will correspond to option D in our answer choices. So option D will be the answer to this particular practice problem and that'll be it for this video. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topic. That'll be it for this one. Thank you.