Consider two unequal resistors, of resistance R₁ and R₂, ...

Question

Consider two unequal resistors, of resistance R₁ and R₂, that are connected either in series or in parallel. Fill in the Table below assuming the electric potential on the low-voltage end of the combination is V_A volts and the potential at the high-voltage end of the combination is V_B volts. First draw diagrams.

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Accepted Answer

Welcome back. Everyone in this problem. A physics student is studying series and parallel combinations in his laboratory with two resistors of five and 15 ohms. He connects them in series and parallel and keeps the low voltage end at zero volts and a high voltage and at four volts in each case afterward, he measures the currents through the resistors correctly. In both cases, what should his measurements be? A says that in series the current to the five ohm resistor and 15 ohm resistor, 0.4 amps while in parallel they are 0.8 and 0.27 amp B says that in series is 0.2 and 06 amps while in parallel 0.8 and 0.25 amps. C says in series 0.2 amps for both while in parallel 0.8 amps and 0.27 amps. And the D says that in series 0.2 amps for both while in parallel 0.25 and 0.27. Now, if we're going to figure out the value of the current to the resistors in both cases, it helps if we draw the both of them in the configurations to understand exactly what's going on. So let's start with our resistors connected in series. OK. So in this scenario, as we said, we know that our student has two resistors. OK. And one is five ohms, the other is 15 ohms. And the low voltage end is at zero volts while the high voltage end is at four volts. So in this series configuration, what will be the current through our five ohm resistor? OK. And our 15 ohm resistor. Well, if we think about it, since they're connected in series, it's going to be the same current that's flowing through our resistance. OK. So once we find the equivalent resistance of our configuration, then we should be able to find the current. And because they are in series, then the equivalent resistance is going to be equal to the sum of our resistors five ohms plus 15 ohms which is 20 ohms. OK. So that means then that I five ohms equals I 15 ohms, which would be the voltage which is four volts divided by the equivalent resistance of 20 ohms which equals 0.2 pi so in series, the current through both resistors is 0.2 amperes. Now, what if they were connected in parallel? Well, again, let's draw a circuit or configuration that represents a parallel or resistors in parallel. OK. So now in this case, we have our voltage source and now it goes to our connection. OK. So we're gonna have one resistor like this and the other like this. OK. And we have our other voltage end. So now let's say the one at the top is five ohms, the one at the bottom is 15 ohms. And we have our potential difference of volts. OK. So now that we have here a potential difference between our terminals as four volts. How are we going to figure out the currents with a five and 15 ohm resistor? Well, we know that when they are connected in parallel, the potential difference is the same for both resistors. OK. Or across both our resistors. And since the potential difference is the same, OK. And we know that the current is equal to the voltage divided by the equivalent resistance. In this case, we're gonna be talking about the value of both our resistors here. Then if we keep the voltage with the same, we can find the current for our varying resistors because no, that means the current for our five ohm resistor will be four volts divided by five ohms which equals 0.8 S. While the current through our 15 ohm resistor equals four volts divided by 15 ohms which equals 0.267 pires or approximately 0.27 pires to two significant figures. So what does this tell us? Well, in series, the current through the resistors are 0.2 amperes. While if they are connected in parallel. The current through the five ohm resistor is 0.8 amperes and the current through the 15 ohm resistor is 0.27 amperes. If we look back at our answer choices that tells us that c is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Ohm's Law

Series and Parallel Circuits

Voltage Division and Current Division

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