Light Bulbs in Series and in Parallel. Two light bulbs have constant resistances of 400Ω and 800Ω. The two light bulbs are connected in series across a 120-V line. Afterwards, the two light bulbs are connected in parallel across the 120-V line. (g) In each situation, which of the two bulbs glows the brightest?

Video transcript

Hey everyone in this problem we have a circuit that contains two resistors. R 1 220 OEMs and R. Two which is equal to 350 homes. A switch on the board determines if the resistors are connected in series or in parallel. The circuit is powered using 110V for the series. And parallel connections were asked which resistor generates more heat so which resistor generates more heat in each of these cases. Now when we're talking about generating more heat, okay, this means that we have more power output. Okay, if we have more power output then we have more heat. So how do we calculate the power output? Well, the power output P is going to be equal to the voltage V times the current. I the potential V. Now according to this law, we have a relationship between V. I and R. And so we can also write the power as V squared over R. Or as I squared times R. Okay. Depending on what information we have. So let's start in series. Okay. Now in series we know that the current through the resisters is the same. Okay, so if we know the current through the resistors is the same. We have information about the current. I. So let's use the equation that has I in it. Okay. As well as our because we're looking at the resistors so we're gonna use P is equal to I squared R. Now we know that I is the same for both resistors. So which resistor is going to give us a larger B well a bigger are Okay, is going to imply a bigger p which implies that we have more heat. So which resistor is larger? Which resistance is larger? Well, it's going to be our two of 350. Hopes If you substitute 350% into this problem, you're going to get a larger power than if you substituted 220 homes because you're multiplying. All right, so that's it for serious. What about in parallel? In parallel? What do we know in series? We use this idea that we know that the current through the resistor is the same in parallel. We know that the voltage is going to be the same. Mhm. Now, if we know the voltage is the same, let's use the equation that has voltage and resistance are we know that the power output is going to be v squared over. R. Now we're dividing by our Okay, so we actually want a smaller, A smaller are is going to give us a bigger and I forgot to write p appear bigger piece. So the bigger are in series resulted in a bigger power output P which resulted in more heat. In this case a smaller are results in a bigger p which results in more heat. Okay, so we're dividing by arc. So if you divide by a smaller number, you're gonna get a larger result larger power means more heat. Okay, so in this case we want our one which was 220. OEMs, because that is smaller than the resistance are two of homes. Alright? So if we look at our answer choices, Okay. We found that if we were in series we wanted to take the resistor which with a larger resistance which was 350 homes. And if we were in parallel we wanted the resistor with the smaller resistance, which was 220 homes. And so we have option. C. Thanks everyone for watching. I hope this video helped you in the next one.