There's all kinds of different ways to hook up multiple capacitors. But if capacitors are connected one after the other in this way, we call them capacitors hooked up in series.
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So say you were taking a test, and on the test it asked you to find the charge on the leftmost capacitor. What some people might try to do is this. Since capacitance is the charge divided by the voltage, they might plug in the capacitance of the leftmost capacitor, which is 4 farads, plug in the voltage of the battery, which is 9 volts. Solving for the charge, they'd get that the leftmost capacitor stores 36 coulombs, which is totally the wrong answer. To try and figure out why and to figure out how to properly deal with this type of scenario, let's look at what's actually going on in this example.
When the battery's hooked up, a negative charge will start to flow from the right side of capacitor 3, which makes a negative charge get deposited on the left side of capacitor 1. This makes a negative charge flow from the right side of capacitor 1 on to the left side of capacitor 2. And that makes a negative charge flow from the right side of capacitor 2 on to the left side of capacitor 3. Charges will continue doing this. And it's important to note something here.
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Because of the way the charging process works, all of the capacitors here must have the same amount of charge stored on them. It's got to be that way. Looking at how these capacitors charge up, there's just nowhere else for the charge to go but on to the next capacitor in the line. This is actually good news.
This means that for capacitors in series, the charge stored on every capacitor is going to be the same. So if you find the charge on one of the capacitors, you've found the charge on all of the capacitors. But how do we figure out what that amount of charge is going to be? Well, there's a trick we can use when dealing with situations like this.
We can imagine replacing our three capacitors with just a single equivalent capacitor. If we choose the right value for this single capacitor, then it will store the same amount of charge as each of the three capacitors in series will. The reason this is useful is because we know how to deal with a single capacitor.
We call this imaginary single capacitor that's replacing multiple capacitors the "equivalent capacitor. And it turns out that there's a handy formula that lets you determine the equivalent capacitance. The formula to find the equivalent capacitance of capacitors hooked up in series looks like this. And if you had more capacitors that were in that same series, you would just continue on this way until you've included all of the contributions from all of the capacitors.
We'll prove where this formula comes from in a minute, but for now, let's just get used to using it and see what we can figure out.
- Kondensatorer i parallel (video) | Circuits | Khan Academy.
- Capacitors in series (video) | Circuits | Khan Academy!
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Using the values from our example, we get that 1 over the equivalent capacitance is going to be 1 over 4 farads plus 1 over 12 farads plus 1 over 6 farads, which equals 0. You're not done yet. We want the equivalent capacitance, not 1 over the equivalent capacitance. So we have to take 1 over this value of 0. And if we do that, we get that the equivalent capacitance for this series of capacitors is 2 farads.
Now that we've reduced our complicated multiple capacitor problem into a single capacitor problem, we can solve for the charge stored on this equivalent capacitor. We can use the formula capacitance equals charge per voltage and plug in the value of the equivalent capacitance. And we can plug in the voltage of the battery now because the voltage across a single charged-up capacitor is going to be the same as the voltage of the battery that charged it up.
Solving for the charge, we get that the charge stored on this equivalent capacitor is 18 coulombs. But we weren't trying to find the charge on the equivalent capacitor.
We were trying to find the charge on the leftmost capacitor. The exact value of the resistor is not critical but I would keep it in the k ohm range. I would recommend getting a 1 watt resistor if possible your capacitor may have come with a resistor for charging. A lower wattage resistor will heat up too quickly. Also, do not hold the resistor with your bare hand. The current flowing through the resistor will cause the resistor to heat up and you could be burned.
A good place to put the resistor is in the main power wire fuse holder the one installed near the battery. Simply substitute the resistor for the fuse. A diagram for the capacitor charging setup is shown below. You will need to place a voltmeter across the capacitor to monitor the voltage.
Circuits with capacitors
Once the voltmeter reads 12 volts or close to it you can remove the voltmeter and replace the resistor with the power fuse. Alternatively you can measure the voltage across the charging resistor.
It should start around 12 volts and slowly work its way down to 0 volts. When the voltage stops changing you have charged the capacitor completely.
Capacitors and capacitance (video) | Khan Academy
Another method for charging involves using an old style test light instead of a resistor. The connection is similar alligator clip on one side, probe on the other but you don't need a voltmeter to monitor voltage. When the bulb goes out the capacitor is charged because the voltage across the bulb went from 12volts to 0volts.
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