In the circuit shown in Fig. E26.27

find (b) the unknown emfs ε_1 and ε_2.

Video transcript

Welcome back, everybody. We are taking a look at this circuit right here with these two batteries and we are tasked with finding what the electro motive forces are of each of our batteries. We're gonna do this is we're going to use the loop rule and the junction rule as well. So let's go ahead and try to find the electro motive force of our battery over here. I'm gonna mark both loops in the same direction just for the sake of being easy here. Let's look at loop one. What do we have? We have that E one minus eight times 1.75. That's gonna be the voltage of this resistor up here - times. The current flowing through this center section is equal to zero. What is the current flowing through the center section? Well, according to the junction rule, the sum of all currents going into and out of a junction need to be zero. So we have 1.75 going in, we have 1.25 going out plus our eye that we need to find going this way, this is gonna be our I is equal to zero. When we add and subtract to the appropriate side, we get that our current is negative 0.5, which just means it's going out of the junction in this direction and it is 0.5. Let's go ahead and plug in 0.5 right here. We then get that E one is equal to 14 plus four, which gives us 18 volts as our first electro motive force. Great. So now let's go ahead and look at loop two for E two going this direction we are entering in the positive side of the battery leaving the negative side of the battery. So this will be negative. We have negative E two plus. Since we're going against the current here is 20.5 times eight minus 1.25 times one, which is the voltage of this resistor up here. This is equal to zero from this. We get that E two is equal to four minus 1.25 giving us an electro motive force of 2. volts. So now we found the electro motive force of battery one and the electro motive force of battery to giving us a final answer. Choice of C. Thank you all so much for watching. I hope this video helped. We'll see you all in the next one.