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Problem 24 Hard Difficulty

Four resistors are connected to a battery with a terminal voltage of 12 $\mathrm{V}$, as shown in Figure P 18.24. (a) How would you reduce the circuit to an equivalent single resistor connected to the battery? Use this procedure to find the equivalent resistance of the circuit. (b) Find the current delivered by the battery to this equivalent resistance. (c) Determine the power delivered by the battery. (d) Determine the power delivered to the $50.0-\Omega$ resistor.

Answer

a. 60.0 \Omega
b. 0.20 A
c. 2.4 \mathrm{W}
d. no answer available

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Video Transcript

to find effective distance in this particular problem. As shown in figure, be eating 0.24 Let us consider the conventional direction of the current first. Now we, Frist, you kill the current I, which is a main current delivered by the battery. Now this particular current is getting sprayed into drug companies. The first run let it be I want. And the 2nd 1 which is flowing through 50 0 Manito Audio be. I do no. Since the same current to flow stuff off the interview. These two real distances are insidious. Sufferers will write it. Let for a step, eh? Let r s that. The city's combination of the resistance is equal to do 50 last 30 which is equal to idioms now when we draw the diagram with respect with that, it would be something like this. Get a three ra distances which are connected. I shone anyone battery which is off to avoid. Now this will be your artists which is off idioms. The 2nd 1 is off idioms again. And this one which is connected in cities with the battery which is off 20 homes. This is the current I, which is a main current. And these are It's two components Ivan and the upper one is I do. Now, in order to find the pattern combination off to ADM Red Distances, we'll write it as let the effective resistance. Oh, artists and idioms be R B. She's right here in the next day as our easy quit, too. Artists battling to idioms this our eases off idioms that we already got. So that indicates 80 almost battling to legumes. And we need to use the formula, as in the new monitor we righted as 80 multiplied by 80 upon edition on these two distances in the answer that we get as 40 homes. So therefore, partner combination off distances is off 40 homes, though this is not to find an answer because there is one more resistance, which is off 20 jobs. It's calculated that first we'll draw the dagger out 40 homes. That is the value of our P matches, definitely in CDs with to end your arms found in CDs with troubled. And when we consider the current I now, which is flowing through 20 as well as 40 homes. No, we're right. They're coming does since same current I feels two 40 homes and 20 homes dead for Let's That resistance Be Are effective, sir. It is 40 less trendy because off 60 homes. Now let's draw the are effective resistance with respect to your battery. So this is effective. Rick is off 60 homes in the Battery off 12 World. He's attached to it. The girl's got into I so this we have got the answer to step a as if it to resistance off the end. Oh so good is off 60 homes. This is ah, state. A answer. Let's move to the step be We need to find the current delivered by the battery. So let Guidant did. He would. Bye battery off 12 balls. B I. We take the nomination as I using simple homes. Oh, that is We's equal to ay and do resistance, but here it will be the entire is and that is our effective, which we have already found out. So therefore, 12 volt is equal to I and multiplied by 60 homes. Therefore, eyes equal to 12 would divided by 60 rooms. Finally, we get the total current value I, as Zito point to amperes, and this is our answer to step. Be now. Let's move. Two steps. See? We need to calculate power delivered by the battery off. Well bowled. So this is your amulet, Bauer. Do you would. Bye. The battery be B 12 volt. So we'll use the formula for power. That is B 12 old is equal to Weren't age multiplied by the current? Not here. Batteries off 12 World. So right, well won't on current did he would buy the battery is a CDO 0.2 am PIAs which we have got as an answer instead be when the calculate days we get the value as 2.4 words. Therefore, we're right down soon as power delivered by the battery off World Wars is off to a point four words. This is the answer for step. See, let's move it in the steppe d, we need to calculate the power daily word to the 50 on red distance. So lyricism Let our daily word two the 50 own register be B 50 homes. This innovation that we're taking Let's draw the diagram first You understand the concept behind it. There are two distances brother in the upper branches, dinner to re distances and the steward of the senses aren't battling with idiom resistance. I shone in the original figure, so let's explore that first. And there is one more resistance, which is off 20 home riches in CDs with the battery or your current is off. I and we all really mation to Karen's, which are flowing as Ivan I do. And this order's no current is getting back. Did the negative terminal of the bacteria's by the conventional direction of the current, which is off I cremation. It does I. So this marriage, when he does I now we need to first calculate the world is a gross Tony Olds. So this is again simply by OEMs law, that is, I multiplied by our he's equal to ay mighty plan by our so we train your music will do the current, which is flowing through 20 arms. So I might be blamed by train value off I. We already got it as 0.2 on beers multiplied by 20 homes. Therefore, the value off 20 is four words. No, since this is a circuit having certain combination in CDs, wordage is getting speeded into the different components. So, aspirin this concept can we see that will get a gross 80 homes. Bless. We'll get across 20 homes is equal to the main voltage mitt is off 12 worlds. That means 12 World is getting speeder across 80 homes and 20 homes. Therefore, let's calculate the value of old age across idioms first. So we idioms is equal to 12 worlds, minus re 20 homes, which is equal to 12 wars minus four words. Therefore, Rhea Doom's is equal to eight wounds. This is the value of voltage across idioms. No, in order to calculate the current, which is flowing through 50 home and 30 on since your deal and the combination of 50 interview rooms are in Parliament, they share the same war dish. So to calculate the value off too I do is equal to hear We're making use of simple homes law that his musical trying to our So I becomes be a diem's and combination off distances to Richard. It's going so we d is eight wards born eight Humes. So therefore, we're getting the value s 0.2 on ampere, therefore, couldn't two frisky home is CEO point to one amperes Now, finally, we need to calculate the power to leeward to the 50 ominous distance. So we make use off the formula because be 50 home is equal to current which is flowing through it. The square off it, the city's information. I drew square Mikey, blind by its resistance When you so modify to be already go to does 0.2 on ampere and the squared off it my deployed by 50 homes. Careful Bauer daily work it off of camera. Distance is equal to 0.5 warts. This is the value which you have got is an answer could be

Top Physics 102 Electricity and Magnetism Educators
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