Resistor Combinations

1/R_parallel = 1/R_a + 1/R_b

R_parallel = (R_a*R_b)/(R_a + R_b)

What If You Have A More Complex Circuit

Here's a circuit with resistors that has them connected in a different way. For a short while we're going to work on the question of how to analyze this circuit. For a start we're going to assume that this is a resistor. It has two leads at the left (marked here with red dots) and we'll assume that we want to find the equivalent resistance you would have at those leads.

We will use the following numerical values for the resistors in this example, and we will work through using these values.

• R_a = 1500 W

• R_b = 3000 W

• R_c = 2000 W

• R_d = 1000 W

• V_s = 12 v

We need to figure out where we can start. We can start by trying to find any of the combinations we've learned about. So let's think about whether there are any series or parallel combinations and if there are let's see if we can identify them. Then we can apply what we know about series and parallel combinations. There's no guarantee that approach will work, but it is worth a try. Let's look at two resistors at a time.

The first question is are there any series or parallel combinations? Click the red button below to see two resistors in series.

Question

Q6 Would the two resistors above (highlighted when the button is clicked) be in series if any current were drawn from the circuit by attaching a load?

Now, we should be able to replace the two resistors in series with their series equivalent. If we do that, there's a node in the middle with a voltage, and we'll lose information about that voltage. Right now, we're not interested in that voltage, and we'll willing to lose that information. Let's just replace the two resistors with their series equivalent. Click the red button to make that replacement. Depressing the button will remove the two resistors in series, and releasing the button will insert the replacement.

Now you should have the circuit with the two resistors in series replaced by their series equivalent. Now, we can see that there is another replacement we can make. What's that replacement?

Q7 What replacement can be made?

Ok, you see how it goes. Let's take a numerical example using the values mentioned above.

• R_a = 1500 W

• R_b = 3000 W

• R_c = 2000 W

• R_d = 1000 W

• V_s = 12 v

Here is the circuit.