Relationship between current and resistors in parallel

Resistors in Parallel

relationship between current and resistors in parallel

somewhere else in the ciruit. This is known as a parallel connection. Each of the three resistors in Figure 1 is another path for current to travel between points . Knowing that branch currents add up in parallel circuits to equal the total current Rather than being directly proportional, the relationship here is one of inverse Conversely, knowing that total resistance in a parallel (current divider) circuit is . Electronics Tutorial about Resistors in Parallel with Parallel Resistors Connected Together and Resistors Then parallel circuits are classed as current dividers.

In a parallel circuit, each device is placed in its own separate branch. The presence of branch lines means that there are multiple pathways by which charge can traverse the external circuit. Each charge passing through the loop of the external circuit will pass through a single resistor present in a single branch. When arriving at the branching location or node, a charge makes a choice as to which branch to travel through on its journey back to the low potential terminal.

relationship between current and resistors in parallel

A short comparison and contrast between series and parallel circuits was made in an earlier section of Lesson 4. In that section, it was emphasized that the act of adding more resistors to a parallel circuit results in the rather unexpected result of having less overall resistance.

relationship between current and resistors in parallel

Since there are multiple pathways by which charge can flow, adding another resistor in a separate branch provides another pathway by which to direct charge through the main area of resistance within the circuit.

This decreased resistance resulting from increasing the number of branches will have the effect of increasing the rate at which charge flows also known as the current.

In an effort to make this rather unexpected result more reasonable, a tollway analogy was introduced. A tollbooth is the main location of resistance to car flow on a tollway. Adding additional tollbooths within their own branch on a tollway will provide more pathways for cars to flow through the toll station.

These additional tollbooths will decrease the overall resistance to car flow and increase the rate at which they flow. Current The rate at which charge flows through a circuit is known as the current.

Charge does NOT pile up and begin to accumulate at any given location such that the current at one location is more than at other locations. Charge does NOT become used up by resistors in such a manner that there is less current at one location compared to another.

In a parallel circuit, charge divides up into separate branches such that there can be more current in one branch than there is in another. Nonetheless, when taken as a whole, the total amount of current in all the branches when added together is the same as the amount of current at locations outside the branches.

The rule that current is everywhere the same still works, only with a twist. Voltage Divider Formula It is quite easy to confuse these two equations, getting the resistance ratios backwards. One way to help remember the proper form is to keep in mind that both ratios in the voltage and current divider equations must equal less than one.

After all these are divider equations, not multiplier equations!

BBC Bitesize - Higher Physics - Current, potential difference, power and resistance - Revision 1

If the fraction is upside-down, it will provide a ratio greater than one, which is incorrect. Knowing that total resistance in a series voltage divider circuit is always greater than any of the individual resistances, we know that the fraction for that formula must be Rn over RTotal. Conversely, knowing that total resistance in a parallel current divider circuit is always less then any of the individual resistances, we know that the fraction for that formula must be RTotal over Rn.

Current Divider Circuit Example Application: Electric Meter Circuit Current divider circuits find application in electric meter circuits, where a fraction of a measured current is desired to be routed through a sensitive detection device.

Using the current divider formula, the proper shunt resistor can be sized to proportion just the right amount of current for the device in any given instance: So if you think about it, the flow of electrons in this branch plus the flow of electrons in that branch have to add up to the flow of the electrons in this branch, right? And then they're going to meet back up, and then the flow of electrons here-- so if we think of it this way, and now I'm going to go back to the convention, this is I1.

relationship between current and resistors in parallel

So you have these electrons flowing at a given rate. This is the current right here. They're going to branch off, and maybe half of them go-- we'll see if the resistances are equal, if both of these branches have an equal amount of capacity in terms of how fast the electrons can flow through. If they're equal, or since we're going to current in this direction, let's talk about positrons or positive charges.

If the positive charges-- although I just want to keep saying that it is not the positive charges that are moving. But if you say that the lack of electrons can flow equally easily between both paths, that's if the resistances were the same, we could imagine that the current, the flow, would split itself up, and then over here would meet back up. And then we would say that the current here would also be I1. But let's figure out where the current's going.

Calculating Current in a Parallel

Let's call this current I2 and let's call this current I3. So I think it is reasonable, and you can imagine with water pipes or anything, that the current going into the branch is equal to the current exiting the branch. Or you could even think of it that the current entering-- when the currents I2 and I1 merge, that they combine and they become Current 1, right?

I mean, think about it.

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In a given second, if this is 5 coulombs per second-- I'm just making up numbers-- and this is 6 coulombs per second, in a given second right here, you're going to have 5 coulombs coming from this branch and 6 coulombs coming from this branch, so you're going to have 11 coulombs per second coming out once they've merged, so this would be 11 coulombs per second. So I think hopefully that makes sense to you that this current is equal to the combination of this current and that current.

relationship between current and resistors in parallel

Now, what do we also know? We also know the voltage along this entire ideal wire is constant, so then voltage-- let me draw that in another color, in blue.

Current through resistor in parallel: Worked example (video) | Khan Academy

So, for example, the voltage anywhere along this blue that I'm filling in is going to be the same, because this wire is an ideal conductor, and you can almost view this blue part as an extension of the positive terminal of the battery. And very similarly-- I'll do it in yellow-- we could draw this wire as an extension of the negative terminal of the battery. This is an extension of the negative terminal of the battery. So the voltage difference between here and here-- so let's call that the total voltage, or let's just call it the voltage, right?

The voltage difference between that point and that point is the exact same thing as the voltage difference between this point and this point, which is the exact same thing as the voltage difference between this point and this point.

So what can we say? What is the total current in the system? If we just viewed this as a black box, that this is some type of total resistance, well, the total current in the system would be the total voltage, the voltage divided by-- let's call this our total resistance, right?

Let's say we couldn't see this and we just said, oh, that's just some total resistance, and that is equal to the current going through R1. This is a 1 right here. This is current I1. Well, it's going to be the voltage across this resistor divided by the resistance, right? That's what Ohm's law tells us: So I1 is equal to the voltage across this resistor, but we just said that voltage is the same thing as this voltage, right?

The voltage here is the same thing as the voltage here. So the voltage across that resistor is still V, and so the current flowing across that resistor is V over R1.