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Problem 66 Hard Difficulty

Consider the two arrangements of batteries and bulbs shown in Figure P 18.66. The two bulbs are identical and have resistance $R,$ and the two batteries are identical with output voltage $\Delta V .$(a) In case $1,$ with the two bulbs in series, compare the brightness of each bulb, the current in each bulb, and the power delivered to each bulb. (b) In case 2, with the two bulbs in parallel, compare the brightness of each bulb, the current in each bulb, and the power supplied to each bulb. (c) Which bulbs are brighter, those in case 1 or those in case 2? (d) In each case, if one bulb fails, will the other go out as well? If the other bulb doesn’t fail, will it get brighter or stay the same? (Problem 66 is courtesy of $E.$ $F.$ Redish. For other problems of this type, visit http://www.physics.umd.edu/perg/.)

Answer

a. P=\frac{(\Delta V)^{2}}{4 R}
b. \begin{array}{l}{\text { Both bulbs receive the same current and dissipate the same power, and are }} \\ {\text { the same brightness. }} \\ {I=\frac{\Delta V}{K}} \\ {P=\frac{(\Delta V)^{2}}{R}}\end{array}
c. \text { Case } 2 \text { is brighter. }
d. \begin{array}{l}{\text { In case } 1, \text { if one bulb goes out, so will the other. In case } 2, \text { if one bulb goes out, the }} \\ {\text { other will remain at the same brightness. }}\end{array}

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Video Transcript

ask for the given dude. Oh, here The Cubans are identical. Having the same distance are without put shortages. Delta Bi. Now let's start with step, eh? And to find the answer with respect to a swan. Now, in this case, double, they're having the same resistance, so we'll just write it down. Says, do Bubs are having same a distance, and they are connected right here in series. So argument, Lee, the same current flows so right down the same current froze through them. So the potential difference what he means the same it grows, but yeah, and B also we can see that to bugs are equal in brightness because of that. So at the same time, we can add something that is more or power distribution is given as, say, participation is equal to I screwed up so therefore couldn't and registers. Now these two bad amigos in case one are seen, Dad, for this power dissipation, it means the same This we can conclude that both bugs have seem current, huh, Bagger and even equal brightness in case one. This should be though answer now that's moving the next beach and try to find and super step be here. We are going to consider case too. Where bulbs are connecting batter. So right first here to Bob's are in battle in now would add more their resistance and potential difference. All right, seem we write more here. So these two birds, these bulbs d'oh equally? No, Since it grows the true Bubbs, it's same current two. The boats remains the same since they have same traditions. Now let's talk about the power distribution. Also, power dissipation across the bulbs remains the scene now destination that power dissipation is equal to I square multiplied by our should us. Finally, we can see that both bulbs both the bulbs I have same couldn't power and even equal brightness in case too. This is the answer. Now let's move to step three and write down and surf or step See, that's captured governed in each case now. So here, if you consider the case one and we're right against you, Cigar and I s is equal to Delta. We upon two games are because bulbs are connecting cities and here began mation. It does say I'd be one is equal to I P too. Is Delta v upon our so we can see that I p one is this current and I bread was this current since warded across both of them remains the same and they're having the same the distance. We can say that simply using home slow but Delta bi upon our in case too. Now let's write down something to explain So and this would be very important we can mation God didn't flows through each of this show. Specifically in case too is devil do that off in case one we need to understand this because in case to a distance is half of the geese one so current will be doubled. Nix signboard barber supplied is equal to is basically I square market power. Better distance. So what we can say that does increase do power supplied to each bug is four times to the power to each bug in case one. Now here the boat having more power definitely has more brightness, So no, but in case too. Okay, so we're writing the bulge in case too with the deal brighter then that off in case one, this is what weekend Right now let's go to page for to write down the answer first MD Now here we get nation directly about case one encased. You sold her first, right? About case one. So, in case one, since the bugs are connected and see the sword right down says the bulbs here, uh, being series, the same gun flows through them. So if any, we're right here off the bugs. So if any of the bulbs is field, God didn't cannot feel two The part because our fridge that either by I could not glow. This is what you need to understand. Since the same current flow straight. This could be the answer for the case. One. We're right on the next page for gays to soo in case, too, which is a battery circuit. We're right here, since the bulbs are connected in battle in if the pot through which couldn't flows. Two. The but A is broken then but a they're not go, but but be. But glow continuously says it's spot Couldn't it means the scene that's a legitimately God didn't two but be remains the same and pretty close with same brightness. Even if the bulb is not working

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