Anderson Video - Internal Resistance

Professor Anderson
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Let's talk about internal resistance. And this is what is the resistance inside of the battery. So a battery, the way we've drawn it, the ideal battery just looks like this. It is a voltage supply V, there is positive on one side, negative on the other, but that's not really what's in a battery. A real battery has some internal resistance to it. So a real battery should really be modeled as this a voltage plus an internal resistance. And that's this little lowercase r. What is the resistance inside a battery? So if you have an ideal voltage supply, then that internal resistance is zero. And what it means is no matter what you connect to the battery, it's always going to be the same volts. Your 12-volt car battery, if you attach loads to it it's still going to be 12 volts. But in reality, r is never zero. And for a car battery, r is approximately .01 ohms. It's something pretty small, but it is still real. Now V of the battery is what's coming out here. What's coming out of the circuit, out of this circular region, is what you actually measure coming out of the battery. It's not only a voltage supply, it's a little internal resistance. And we call that the terminal voltage. So, we know what that is because we know what Ohm's law says. The battery terminal voltage is going to be the following. It's this ideal V minus the voltage drop across the resistor, and Ohm's law tells us that it is I times R. So, if you're not drawing any current out of your battery then the voltage is 12 volts. But as you start to draw more and more current out of the battery, the voltage drops a little bit. So let's see what it drops to when we are starting the car battery. When we're starting the engine using the battery as a current supply. Okay, so what we said in class was during start, that thing can be drawing 300 amps. So what is the voltage on those terminals? V on the terminals is going to be V minus IR which is 12 volts, minus I, 300 amps, times a little r which we said was 0.01 ohms, and so we get 12 volts minus let's see, 300 times 0.01 is 3, right? That's a hundredth. Amp times ohms is also volts, and so you get 9 volts. And you can measure this. You guys have a little voltmeter, probably at home you have one that you're playing with in the lab. If you connect this to your car battery and you look at the voltage on your car battery it's going to read around 12 volts. But when you start the car that voltage is going to lower to about 9 volts. After the car starts and this current goes back to zero, then it'll go back up to 12 volts. It's kind of a fun little experiment to do
Let's talk about internal resistance. And this is what is the resistance inside of the battery. So a battery, the way we've drawn it, the ideal battery just looks like this. It is a voltage supply V, there is positive on one side, negative on the other, but that's not really what's in a battery. A real battery has some internal resistance to it. So a real battery should really be modeled as this a voltage plus an internal resistance. And that's this little lowercase r. What is the resistance inside a battery? So if you have an ideal voltage supply, then that internal resistance is zero. And what it means is no matter what you connect to the battery, it's always going to be the same volts. Your 12-volt car battery, if you attach loads to it it's still going to be 12 volts. But in reality, r is never zero. And for a car battery, r is approximately .01 ohms. It's something pretty small, but it is still real. Now V of the battery is what's coming out here. What's coming out of the circuit, out of this circular region, is what you actually measure coming out of the battery. It's not only a voltage supply, it's a little internal resistance. And we call that the terminal voltage. So, we know what that is because we know what Ohm's law says. The battery terminal voltage is going to be the following. It's this ideal V minus the voltage drop across the resistor, and Ohm's law tells us that it is I times R. So, if you're not drawing any current out of your battery then the voltage is 12 volts. But as you start to draw more and more current out of the battery, the voltage drops a little bit. So let's see what it drops to when we are starting the car battery. When we're starting the engine using the battery as a current supply. Okay, so what we said in class was during start, that thing can be drawing 300 amps. So what is the voltage on those terminals? V on the terminals is going to be V minus IR which is 12 volts, minus I, 300 amps, times a little r which we said was 0.01 ohms, and so we get 12 volts minus let's see, 300 times 0.01 is 3, right? That's a hundredth. Amp times ohms is also volts, and so you get 9 volts. And you can measure this. You guys have a little voltmeter, probably at home you have one that you're playing with in the lab. If you connect this to your car battery and you look at the voltage on your car battery it's going to read around 12 volts. But when you start the car that voltage is going to lower to about 9 volts. After the car starts and this current goes back to zero, then it'll go back up to 12 volts. It's kind of a fun little experiment to do