In the circuit shown in Fig. E26.23, ammeter A1 reads 10.0 A and the batteries have no appreciable internal resistance. (a) What is the resistance of R?

Video transcript

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use. In order to solve this problem. A student made the electric circuit as shown in the figure below to measure the value of an unknown resistor R subscript A that is using ideal batteries. The red amateur indicates a value of 2.25 years. Find the resistance of R A. Awesome. So we're given a figure that of the electric circuit that the student created. So we have our red AM ammeter shown on our circuit and it's for 2.25 amp here. And then it shows with this jagged line, the resistor R A and then to the right of R A, we have another resistor for 25 ohms. And then on the far right, we have a battery for 11 volts. And then on the bottom left hand corner of our circuit, we have a battery for 14 volts. Awesome. So we're given some multiple choice answers too. Let's read them off to see what our final answer might be. And note that these are all the values for the resistor R A and they're all in the same units of ohm. So let's read them off to see what our answer might be. A is 1.00 B is 4.89 C is 6.22 and D is 11.1. Ok. So first off, let us note that the batteries and the amateur do not have significant internal resistance to help us be better visualize this problem. Let us indicate the direction of loop one as clockwise and draw this inner figure. So I've gone ahead and redrawn the students circuit electric circuit here again off to the right of our diagram that was provided to us, the blue arrow indicates the direction and then we have the co co the clockwise arrow shown in black. So we're gonna follow the blue arrow and go to in the right clockwise direction. So we're gonna go up through the am ammeter through the resistor R A down and around to the far left of our circuit. We're not gonna bother with the right side of the circuit. OK. So now we can apply the loop rule to our loop number one. So let's do that. So we have our positive 14 volts means it's going from the right direction, not the left direction minus 2.25 years for amateur value multiplied by our resistor R A is equal to zero. Now, we can rearrange this equation to solve for R A. So let's isolate and sulfur R A. And we'll get that R A. Our resistor is equal to 14 volts divided by 2.25 amp here. So when we plug that into a calculator, we will get 6.22 ohms. And that is our final answer. We'll box it in green. Awesome. So let me look at our multiple choice sensors. That means the correct answer is cr A is equal to 6.22 ohms. So the resistance of R A is 6.22 ohms. Thank you so much for watching. Hopefully, that helped and I can't wait to see you in the next video. Bye.