# Series And Parallel Capacitance Pdf

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*A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals.*

- Electrostatic Potential and Capacitance
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- Series And Parallel Circuits Worksheet Answer Key Pdf

*Several capacitors can be connected together to be used in a variety of applications.*

## Electrostatic Potential and Capacitance

Track My Order. Frequently Asked Questions. International Shipping Info. Send Email. Mon-Fri, 9am to 12pm and 1pm to 5pm U. Mountain Time:. Simple circuits ones with only a few components are usually fairly straightforward for beginners to understand. But, things can get sticky when other components come to the party. Where's the current going? What's the voltage doing? Can this be simplified for easier understanding? Fear not, intrepid reader. Valuable information follows.

You may want to visit these tutorials on the basic components before diving into building the circuits in this tutorial. Before we get too deep into this, we need to mention what a node is. It's nothing fancy, just representation of an electrical junction between two or more components. When a circuit is modeled on a schematic, these nodes represent the wires between components. Example schematic with four uniquely colored nodes. That's half the battle towards understanding the difference between series and parallel.

We also need to understand how current flows through a circuit. Current flows from a high voltage to a lower voltage in a circuit. Some amount of current will flow through every path it can take to get to the point of lowest voltage usually called ground.

Using the above circuit as an example, here's how current would flow as it runs from the battery's positive terminal to the negative:. Current indicated by the blue, orange, and pink lines flowing through the same example circuit as above. Different currents are indicated by different colors. Notice that in some nodes like between R 1 and R 2 the current is the same going in as at is coming out.

At other nodes specifically the three-way junction between R 2 , R 3 , and R 4 the main blue current splits into two different ones. That's the key difference between series and parallel! Two components are in series if they share a common node and if the same current flows through them. Here's an example circuit with three series resistors:. There's only one way for the current to flow in the above circuit.

Starting from the positive terminal of the battery, current flow will first encounter R 1. From there the current will flow straight to R 2 , then to R 3 , and finally back to the negative terminal of the battery.

Note that there is only one path for current to follow. These components are in series. If components share two common nodes, they are in parallel. Here's an example schematic of three resistors in parallel with a battery:. From the positive battery terminal, current flows to R The node that connects the battery to R 1 is also connected to the other resistors.

The other ends of these resistors are similarly tied together, and then tied back to the negative terminal of the battery. There are three distinct paths that current can take before returning to the battery, and the associated resistors are said to be in parallel. Where series components all have equal currents running through them, parallel components all have the same voltage drop across them -- series:current::parallel:voltage.

From there we can mix and match. In the next picture, we again see three resistors and a battery. From the positive battery terminal, current first encounters R 1. But, at the other side of R 1 the node splits, and current can go to both R 2 and R 3. The current paths through R 2 and R 3 are then tied together again, and current goes back to the negative terminal of the battery. In this example, R 2 and R 3 are in parallel with each other, and R 1 is in series with the parallel combination of R 2 and R 3.

When we put resistors together like this, in series and parallel, we change the way current flows through them. In other words, there's still only one path for current to take and we just made it even harder for current to flow. How much harder? To put this equation more generally: the total resistance of N -- some arbitrary number of -- resistors is their total sum.

What about parallel resistors? Now there are two paths for current to take. But, so is the second resistor, and we now have a total of 2mA coming from the supply, doubling the original 1mA. What then? However, this method is only good for two resistors in one calculation. We can combine more than 2 resistors with this method by taking the result of R1 R2 and calculating that value in parallel with a third resistor again as product over sum , but the reciprocal method may be less work.

You may notice that the resistance you measure might not be exactly what the resistor says it should be. Resistors have a certain amount of tolerance , which means they can be off by a certain percentage in either direction. Thus, you may read 9. As long as it's close to the correct value, everything should work fine. The reader should continue this exercise until convincing themselves that they know what the outcome will be before doing it again, or they run out of resistors to stick in the breadboard, whichever comes first.

Then measure. Repeat the exercise now with 3, 4 and 5 resistors. Did everything come out as planned? If not, go back and check your connections. Go have a milkshake before we continue. There are a few situations that may call for some creative resistor combinations.

And while we can get a very high degree of precision in resistor values, we may not want to wait the X number of days it takes to ship something, or pay the price for non-stocked, non-standard values. So in a pinch, we can always build our own resistor values. Know what kind of tolerance you can tolerate. For example, if you needed a 3.

That would give you 3. But part manufacturers are known to make just these sorts of mistakes, so it pays to poke around a bit. This sort of series and parallel combination of resistors works for power ratings , too. Not pretty, but it will get us through a final project, and might even get us extra points for being able to think on our feet.

We need to be a little more careful when we combine resistors of dissimilar values in parallel where total equivalent resistance and power ratings are concerned. It should be completely obvious to the reader, but The combined resistance of two resistors of different values is always less than the smallest value resistor. The total parallel resistance will always be dragged closer to the lowest value resistor.

Do yourself a favor and read tip 4 10 times over. The power dissipated in a parallel combination of dissimilar resistor values is not split evenly between the resistors because the currents are not equal. But tips 1 and 3 offer some handy shortcuts when the values are the same. Combining capacitors is just like combining resistors Why would this be?

The greater the value of capacitance, the more electrons it can hold. If the size of the plates is increased, the capacitance goes up because there's physically more space for electrons to hang out. And if the plates are moved farther apart, the capacitance goes down, because the electric field strength between them goes down as the distance goes up.

Remember that in a series circuit there's only one path for current to flow. It follows that the number of electrons that are discharging from the cap on the bottom is going to be the same number of electrons coming out of the cap on the top. So the capacitance hasn't increased, has it? By placing the capacitors in series, we've effectively spaced the plates farther apart because the spacing between the plates of the two capacitors adds together. The upshot of this is that we add series capacitor values the same way we add parallel resistor values.

Both the product-over-sum and reciprocal methods are valid for adding capacitors in series. But it should be pointed out that one thing we did get is twice as much voltage or voltage ratings.

Just like batteries, when we put capacitors together in series the voltages add up. Adding capacitors in parallel is like adding resistors in series: the values just add up, no tricks. Why is this?

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Determine the capacitance of a single capacitor that will have the same effect as the combination. Known : Advertisement Advertisement. Wanted : The equivalent capacitance C. Solution :. Capacitor C 2 and C 3 connected in parallel. The equivalent capacitance :. Capacitor C 1 and C p connected in series.

4 in parallel: C. = 10 + 10 = 20 μF. ◇C. 1., C. , C. 2 in series. →How much charge provided by battery to fully charge capacitors? Assume V = ◇Q = C.

## Series And Parallel Circuits Worksheet Answer Key Pdf

Several capacitors may be connected together in a variety of applications. Multiple connections of capacitors act like a single equivalent capacitor. The total capacitance of this equivalent single capacitor depends both on the individual capacitors and how they are connected.

#### Chapter Chosen

These solutions for Capacitors are extremely popular among Class 12 Science students for Physics Capacitors Solutions come handy for quickly completing your homework and preparing for exams. Also, we know that the electric field inside a capacitor is zero. Since capacitance is a proportionality constant, it depends neither on the charge on the plates nor on the potential. It only depends upon the size and shape of the capacitor and on the dielectric used between the plates. It is given that the plates of the capacitor have the same charges.

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