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In the circuit of Figure $19.66,$ find (a) the current through the 8.0$\Omega$ resistor and (b) the total rate of dissipation of electrical energy in the 8.0$\Omega$ resistor and in the internal resistance of the batteries. (c) In one of the batteries, chemical energy is being converted into electrical energy. In which one is this happening and at what rate?

a. 0.40$A$b. 1.6 $\mathrm{W}$c. 4.8 $\mathrm{W}$

Physics 102 Electricity and Magnetism

Chapter 19

Current, Resistance, and Direct-Current Circuit

Electric Charge and Electric Field

Gauss's Law

Electric Potential

Capacitance and Dielectrics

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Electromagnetic Induction

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we are giving the second with with a 12 world battery off internal assistance one home and, uh, eight for battery with internal assistance One home which are connected to an external resistance Off able you are This is two. This is a long one. I'm sorry. And this is our own. And our now for by a A you want to find out the current through the younger sister. Let's say this is the current and the cause and a lot of ways. So we use the key just kinda jobs. Look, law, as usual, let's start with the 12 worlds we have full world and we have for our minus eight times the current because the current is in the same direction Off our Luke, we have the eight for diary which is in the opposite direction. So that's a minus eight and we have to re sisters one on each where the current is in the direction of our law, which gives us minus one eye on minus one. Eye is equal to zero. Excuse us for is equal to 10 I, which means the current is here a point for ampere on notice that the number is positive with means. The direction of the current is actually anti clockwise. But the current is going this way and your sister now for part B you want to find out the power dissipated in all the three sisters. Now we know that power is I square. Are so or the three sisters. We think we add the powers That's I square. I just want four square times a home for the 1st 3 sister a seat upon four square times, one home for the second sister, the seat of 14 square times, one home for the terror Sister, If you can skip this, you know, you could have escaped this step under it. And the sounds rock on foursquare ate this one. This one, that is I square times the total resistance of the circuit, which is the sums off all their expenses because, as you can see, they're all in Siri's. This is simply they don't want 16 times 10 just 116 more. So this is the rate at which heat energy is produced in the circuit. It energy from this. This on this visitor. As you know, when current passes through them these resistors get heated? Yeah. Now, for part C, this is very interesting. As you can notice for the first battery, the current is going this way. And for the second battery, the current is going this way. If you know how bad his wife you can notice that here this battery is producing current. Whereas this current is running against the battery, which means in this case, chemical energy is being converted into electrical energy. But as in this case, electrical energy is being converting toe chemical energy. That is, the second battery is being charged. Whereas this first battery is being discharged, we simply will have to find out battery for which chemical energy is converted into electrical energy. So we simply consider the 12 old. You know, that power is world age times current. We know the voltage here is forward times together and get 0.4 Appier. Excuse us for 18 What? Now The question is here, but it's interesting to find out what the power off the other battery will be for the other battery. The question ends here, and this is miscellaneous, but the power of the other one battery it's simple again three times I. But the voltage here is eight. Hold instead off 12 or so. That uses three point to what? Now? If you notice it, you can see the 3.2 plus one find six is 4.8. So the chemical energy that is converted into electrical energy here in the larger battery in the more stronger battery is divided off. Some offered is going into heat energy in the resisters and the rest off it is being stored in tow. This battery. So as this perfect Estes just this battery discharged, I'll be it with a little intermediate loss.

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