Ohm's law

0:00- [Narrator] When you attach a voltage source across a resistor, a current runs in the circuit. If you were to increase that voltage, then intuitively, you would expect the current to increase as well, right? But the question is, what is the exact relationship between the current and the voltage?

0:15Or the potential difference across any resistor? That's what we're gonna find out in this video. So how do we do that? Well, let's conduct an experiment. So what we'll do is we'll take different values of voltage across the resistor, and for each value of the voltage, we will measure what the current is, and then we'll try to find a pattern.

0:37And from that pattern, we'll figure out what the relationship between the current and the voltage is. So let's do that. To do this, we need measuring devices. We need a voltmeter. Let's connect that across the resistor. And we need an ammeter. We'll connect that somewhere over here in series with the resistor.

0:55And remember that the voltage across the resistor is pretty much the same as the voltage of the power supply. That's because these devices are pretty ideal. And therefore the electric potential here is pretty much the same as electric potential here. And the electric potential over here is pretty much the same as the electric potential over here.

1:10So the potential difference here is the same as the potential difference here. Okay, and so let's keep track of our variables. We have the first variable, which is the potential difference. This is an independent variable. Why is it independent? Because I can choose what the potential difference is going to be in this circuit across this resistor, by changing the knobs over here.

1:30So I control that. That's independent variable. Then we have the current. The current is a dependent variable. We're not directly controlling the current in this experiment. For a given voltage, there will be some current, it depends on the voltage, that's why it's the dependent variable.

1:47And finally, we have another variable, the resistance. And we want to understand how the current depends on voltage or the potential difference, right? So I have to keep my resistance a constant for this entire experiment. And that's why that is my control. I will use some resistor for this entire experiment, and I will not change that.

2:09So that remains a constant. That's my control. And by the way, the symbols we use over here could be pretty confusing, okay? The V over here represents the quantity, electric potential. Delta is the difference. So delta V represents electric potential difference, or voltage.

2:26And this V inside the bracket, that is the symbol for the unit of voltage, which is volts. So that represents volts. I is a symbol for current, and A is a symbol for the unit of the current, which is ampere. Now of course, over here, we are measuring the current in milliamperes.

2:44Milli means 1000th, and ampere is a huge amount of current. So usually in our circuits, in labs, the currents will be much smaller. And so milliampere is an appropriate unit over here. And of course the unit of resistance, we'll get to that. So we don't know that as of now, okay?

3:02All right, so as we said, we're gonna set different values of voltages and we'll measure what the different currents we get, right? So let's choose four tries. And let's say first we'll do 10 volts, then we'll do 20 volts, 30 volts, and 40 volts. And for each one, let's see what the current is, and then we'll see if we can find some pattern.

3:23Right, and before we start, let's just zoom in over here so that we can see clearly the ammeter and the voltmeter readings. Okay, so let's start. I'm gonna set this to 10 volt, and we should see the voltmeter over here reading 10 volt. And then let's see what the ammeter reads.

3:37All right, setting it to 10 volts. And what do we notice? We notice the ammeter reads, well, it's between zero and 20, 10 milliamperes. So for 10 volt, the current in this circuit is 10 milliamperes. Okay, that's our first try. Now let's turn this knob and set it to 20 volts.

3:57Here we go. And the current is 20 milliamperes. And then we'll set it to 30 volts. And the current is 30 milliamperes. And when we set it to 40 volts, we get the current to be 40 milliamperes. We can take more trials if you want, but this is enough for us. Now maybe you can already see a pattern over here, but the best thing to do is now to actually draw a graph.

4:24So let's do that. So in our graph, we're gonna plot the values of voltage and current. So let's choose our independent variable along the x, or the horizontal, and the dependent variable, the current, along the vertical. And let's put some markings over here. Okay, so let's plot them.

4:41When the voltage is 10 volt, the potential difference across the resistor is 10 volt, the current is 10 milliamperes. And then for 20 volts we have 20 milliamperes. For 30 volts you have 30. And then for 40 volts, you have 40 milliamperes. And so the question is, what's the best fit model over here?

4:57Well, I think you can clearly see the best fit model is a straight line passing through the origin. Now of course, if you were to actually do this experiment in your lab, the values won't be so clean. I mean, there will be some experimental errors, and the devices won't be ideal.

5:11So in a real experiment, you might get points scattered like this. So you may want to take even more tries. But what you will find is that the best fit is indeed a straight line that passes through the origin. Okay, what does that mean? This means that the current increases linearly with the potential difference, right?

5:36Straight line means linear. In other words, the current is directly proportional to the potential difference. And that makes sense, right? Like then we double the potential difference, notice, the current doubles. If we triple the potential difference, the current triples, and so on and so forth.

5:52That is the relationship between the current and voltage across a resistor. But let's quantify this a bit more. What will be the slope of this graph? Well, remember, slope always represents the rise over the run. Our rise over here is the current, and the run over here is the potential difference.

6:10So it's going to be I divide by delta V. And this slope is called the conductance, G. Why is it called conductance? Well, it's a measure of how good a conductor this material is. I mean, think about it. If the graph was having a higher slope, then it means for a given voltage, you get even more current, right?

6:32That means it's a better conductor. So that's why the slope literally represents how good a conductor is, and that's why the slope is called the conductance. And by the way, if you rearrange this equation, you get I equals the conductance times delta V. And notice this has the same form as y equals mx plus b, which is the form of a straight line.

6:51Makes sense, because our graph is also a straight line. Over here, the I is like the y-axis. You have delta V, which is the x-axis, and the slope is G. That's what we found. And what about b? Well, that is zero in our case, because b represents the y-intercept, the point where the graph cuts the y-axis.

7:11And in our case, it passes through the origin. So it cuts the y-axis at zero, and so b is zero. So all of that is a great sense check. But what's important for us is the idea of resistance. That's what we wanna talk about, how much the material resists the flow of current.

7:28And so we define resistance of that material as the reciprocal of conductance. Again, that kind of makes sense, right? If something is a good conductor, it has less resistance. In contrast, if something is a poor conductor, it means it has more resistance. So they're inversely related.

7:46And so we define resistance as just one over the conductance, which means it is the reciprocal of the slope, which means it's going to be delta V divided by I. So what would be the unit of this resistance? Well, from this particular equation, we might say it's volts divide by amperes, in general.

8:07But remember, resistance of an element does not depend on the voltage or the current. It depends upon the element's shape and size, and the material that it's made of. So you can measure it by applying a voltage across it and measuring the current through it, but it does not depend on the voltage or the current.

8:24And so to remind ourselves of that, we give it a different unit altogether. It is called ohms and the symbol for that is capital omega. And if we rearrange this, we'll now get the expression for the current. This is called Ohm's Law. It's named after the physicist, George Ohm, who did a lot of work on this.

8:44And look, it's saying the same thing. The current through the resistor is directly proportional to the potential difference across it. Okay, now that we have Ohm's Law, we can use it to calculate the resistance of the resistor that we used in our circuit. It'll be a great idea to pause the video and see if you can figure that out yourself.

9:03All right, so resistance R is delta V over I. And from this graph, I can calculate what delta V is. That is 30 minus 20, that is 10. And I is again, 30 minus 20, that is 10 milliamperes. So it's 10 volt divided by 10 milliamperes. How much is that? Well, the 10 and 10 cancels out to give you one.

9:23But then remember you have this milli, that's 1000th of an ampere. So that goes into numerator, which means you get 1,000 volt per ampere, or 1,000 ohms. So that is the resistance of the resistor that we used in our circuit. Okay, now a quick thing to make sure that we understand all of this is let's change the resistance to 2,000 ohms, and repeat the entire experiment.

9:53The question for you is, what do you think will now be the values of the current for these different trials? And for this particular resistor, what would the new graph look like? This is the old graph for the 1,000 ohm resistor. What would the new graph for 2,000 ohm resistor look like?

10:09Again, great idea to pause the video, and see if you can answer these questions. All right, so we have doubled our resistance value. Now from Ohm's Law, we can see I is delta V over R. If we double the resistance, then for the same value of delta V, we should get half the value of the current.

10:30Does that make sense? For a given value of the potential difference, the current now will be half as before, because the resistance is doubled. Which means when the delta V is 10 volts, the current would now be not 10, but half of that, five. And at this point, it'll be half of 20, which is 10, and 15 and 20.

10:47So this is what the new values, ideal values look like. And if we plot that over here for 10 volts, we now get five milliamps. And then for 20 volts, we get 10 milliamps. and so on and so forth. You can see, you get a new graph that looks like this. Does it make sense that it has a lower slope than before?

11:08Yeah! Remember, slope of this graph represents how good a conductor it is. Now, a 2,000 ohm resistor is a poor conductor, compared to 1,000 ohm resistor, right? Because it has more resistance. So its conductance must be lower, and therefore you would expect the slope to be lower, so that makes perfect sense.

11:29Finally, devices that obey Ohm's Law are called Ohmic devices. Example of that would be the resistor that we usually use in circuits. Even metallic conductors for that matter, they're all Ohmic. But remember that these devices are only Ohmic for, usually for a given range of voltages.

11:47If you go outside that range, they will stop behaving like an Ohmic device and then they become non-Ohmic, meaning this relationship doesn't hold. And the graph of the current versus voltage outside that range will no longer be a straight line. And of course there are other devices like LEDs and transistors that are used in your computers.

12:05They're completely non-Ohmic. There's no range of voltage for which they behave Ohmic. So the graph for them, for the current versus voltage graph for them, will never be a straight line.