# Ohm's Law and Resistors: Example

by Jared Rovny

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00:01 Let's give this an example shot and see how these laws work together.

00:04 So suppose you have a 12-volt battery and it´s in a circuit with a 2-ohm resistor, which is in series with 2 parallel 4-ohm resistors.

00:13 How much current would then be flowing through the circuit? And in fact, there is some ambiguity here because we have wires that are splitting in one case in the circuit into two parallel paths.

00:23 So by how much current is flowing in the circuit, where asking about how much current is flowing, in the location of the battery and the circuit.

00:31 So using that definition for the current flowing in the circuit, see if you can use Ohm's Law as well as the addition rules that we introduced for resistance and solve for the current in this particular circuit.

00:42 If you´ve done that, it should look something like this.

00:45 In this circuit, like we said we have a battery.

00:49 So we're going to draw a battery like this.

00:51 Again, the side with the bigger line here is going to be our positive side and this will be the negative side in our notation.

00:59 So this battery is connected to a few resistors.

01:02 First of all, it's connected to a 2-ohm resistor.

01:04 This is 2 ohms and this 2-ohm resistor we´ve said is in series with 2 parallel 4-ohm resistors.

01:12 So you have 4-ohm resistor here and a 4-ohm resistor here.

01:16 And this completes our circuit.

01:18 Again, these are each 4, 4 ohms of resistance and we have some voltage here which turns out to be 12 volts so let´s actually write that.

01:31 The question is if we know all of these resistances and we know this voltage is 12 volts, what is the current as flowing? And I mentioned that we have some ambiguity here.

01:43 This current was split and go to this top path into this bottom path, so when we´re asking about the total current here.

01:50 What we´re actually saying is what is the current through this wire here as it´s going past the battery.

01:56 Let´s try to do that. What you would do in a situation like this is first, start combining your resistors.

02:01 So first, we´re gonna combine these two 4-ohm resistors into an equivalent resistance and since they're in parallel we have our addition of resistors in parallel law that one over the total resistance is one over each of the individual resistances which in this case is 1 over 4 plus 1 over 4, which is 2 over 4 or 1/2 and now we're going to do the step which is very, very easy to forget which is that we need to find the total resistance which means we have to flip this, because again we said that one over the total resistance equals one over two.

02:38 So the total resistance is 2 ohms not 1/2. So be careful here. This last step is often forgotten.

02:44 So we have the total resistance which is 2 ohms.

02:46 So now, let´s rewrite our circuit. And now that we've simplify it a little bit.

02:49 We now have a 2-ohm resistor here and now we´re equivalent 2-ohm resistance here.

02:55 This one is our original. We haven´t changed that. We have our new one here.

03:00 and we still have our 12-volt battery.

03:03 So now, we just have one last step to do which is to add these two which are in series now.

03:07 So let´s say the total resistance of these two is simply R1 plus R2 since they are in series.

03:14 The current has to go through each one. So this is 2 ohms plus 2 ohms.

03:19 And this is very simply a 4-ohm resistor.

03:22 So now we can one more time rewrite our circuit being a little bit simpler.

03:27 So now we just have a voltage in series with a 4-ohm resistor.

03:34 So now that we have a buffer voltage and the resistance.

03:38 We can use Ohm´s Law which tells us that V equals I times R.

03:43 Since we´re trying to solve for the current, what we need to do is rearrange this and say that I, the current, will be V the amount of voltage or pressure that we're putting into our system divided by the resistance.

03:53 So for more resistance, we´ll get less current flowing.

03:56 Now that we know these 2 values, we have 12 volts divided by 4 ohms.

04:02 Since we're using all of our standard units, we´ll be able to get 12 over 4 is 3 and then volts per ohm which we've already said for current is amps.

04:10 So here it is, we´ve found the current which is flowing through the system.

04:14 Its 3 amps. And as we´ll see later again, be careful, the current up here split and went through one of two pass.

04:22 So instead of having 3 amps up here and 3 amps down here, you would have some smaller amount of current going through each one and we´ll discuss that in more detail, a little later.

04:32 So this is how you would implement a simple example of Ohm´s Law.

04:37 We have a few resistors all acting together.

04:40 You can break down your circuits step by step by using the additional rules we have for resistors whether it´s in parallel or in series and then come to some equivalent resistance and then find the total current that is flowing through your circuit.

04:53 So this wraps up our summary of how to use the individual values in a circuit as well as Ohm's Law and then how to add resistances and a circuit to find things like the current in that circuit.

05:03 Thanks for listening.

The lecture Ohm's Law and Resistors: Example by Jared Rovny is from the course Circuit Elements.

1. 3 Ω
2. 2 Ω
3. 4 Ω
4. 3.5 Ω
5. 1 Ω
1. 0.67 A
2. 0.77 A
3. 0.55 A
4. 0.88 A
5. 0.35 A

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