 Well, I thought I would do a quick video because this question comes up a lot with my students and actually we're doing this right now In my class, so I thought it'd be a good time to work through some stuff. It's the whole idea of your rated Rated power versus your actual power So let me just get this figured out here What I'm gonna do is I'm gonna pull up the old iPad and show you what I'm talking about here So first off, let me just draw this up. I've got a battery here. Let's see. I've got a Resistor we'll call out our baseboard resistor and there's our circuit now say you go to home depot and In the home depot you pick up a heater and it's rated. Let's say this one 2,000 watts At 240 volts Okay, it's common. It's a big one, but it's it's a common Baseboard heater, but let's say that you're not hooking it up to 240 volts Let's say we're gonna hook it up to 208 volts. So let's just change the color So we're gonna actually hook this up to and I know it's a DC circuit But we're dealing with AC when we're dealing with houses. Don't get into that. Let's just talk about the math here Now what I find a lot that happens and this is in my foundation class and then my second year and third year classes are This it's some people automatically want to build a ratio a direct proportion relationship So let me show you Oftentimes when they're doing these questions, they all say okay 240 volts gives me 2,000 watts Therefore 208 volts gives me and gives you this direct proportion But the thing is it's not a direct proportional relationship. You can't go ahead and do that. That doesn't work So the reason why it doesn't work is this little formula here e squared over r equals p this here This e squared throws that whole concept out the window Because if this doubles this doesn't double my power doesn't double if voltage doubles my power quadruple So it's not a direct proportional relationship So you can't go ahead and use something like this and say okay that works So what we're gonna do is we're gonna cut it out. Whoops. Let me just cut that out properly here So they go like this and say bye-bye What we have to do is we have to look at the one thing in this circuit that doesn't change In this unit here So if I went and bought this baseboard heater that is rated to put out 2,000 watts at 240 volts I know that if I mess with the voltage that this is gonna change as well. This goes up This goes up this goes down this goes down the one thing that doesn't change in this circuit is this Let me write this up here. It's your resistance That's the one thing that doesn't change So if the voltage goes up and or down the current goes up or down the power goes up or down That's not a problem, but the resistance is what it is. It's a physical property of the circuit So it doesn't change so when I do these types of questions what I suggest to my students Well, basically a demand of them is to figure out what the resistance of this resistor is and then place it into the new voltage Let me show you what I mean I've got this formula here e squared over r is equal to p right? I'm gonna transpose that to figure out what my r is e squared over p is Equal to r That's just a little bit of transposition So I wouldn't worry too much about how that is if you don't understand how transposition works Make sure you go back and check out the videos on transposition very very important concept to get into your head So we're gonna use that formula first off. So let me just cut this part out here and Move this part up All right, so e squared over p equals r So what we do is we use this here to figure out what the resistance of this base board heater is So we do the calculation here. So that becomes 240 squared over 2000 Equals and we punch in the calculator here showing you how we're doing this all alive and on the fly 240 squared divided by 2000 Equal so this ends up having a resistance of 28 0.8 ohms that's this Resistance of that Heater all right, so we can cut the rest of this out now because we know what this resistance is Let's get rid of all of this oops Delete that out of there. We'll erase this. We know that this has a resistance of 28 0.8 ohms But now we're not putting 240 volts on it We're putting 208 volts on it. So we go back to that formula that we're talking about earlier We know that the formula for power is e squared over r equals p We have our e squared 208 squared Over r which now we know is 28.8 Equals p and in this case we figure out that 208 squared divided by 28.8 equals Basically the power in this one is 15 oh two Point sorry oh two point two Watts and that is how much power is being dissipated across this resistor here When we have it connected to 208 volts there It's not a direct proportion and you see that that makes a big difference because this thing here was Rated at 2,000 watts at 240 volts So we see a big difference there so again whenever we see a question like this where they give you a rating use that rating to work out the resistance and Then use that resistance and plug in the actual voltage that you're using to get the power that easy