When working with circuits that *involve multiple paths* for electricity to take, it is important to understand how to calculate the equivalent resistance between two points.

Circuits can have more than one path for electricity to take, which is why there are cases where you can have multiple outputs from a single input. These inputs and outputs can be **via switches**, IOs, other branches of the circuit, etc.

When there are branches in a circuit, you can figure out the equivalent resistance between two points by using Ohm’s law. Ohm’s law states that voltage (V) equals current (I) divided by resistance (R).

By solving for R, you can find the equivalent resistance between two points in a circuit. Although this article will focus on solving for R in instances of parallel resistors, it can be applied to other instances of circuits as well.

## Next, use the formula for parallel resistors

The next step is to find the equivalent resistance between points a and B. You can do this by finding the total resistance at point A, then finding the total resistance at point B, and then finding the average of these two resistances.

Then, you must calculate what proportion of the total network resistance your *calculated average resistance represents*, and that is your equivalent resistor for this problem.

For example, say you had a network of resistors where the total network resistance was 100 ohms, point A had a resistance of 20 ohms, and point B had a resistance of 30 ohms. To find the equivalent resistor, you *would first calculate* the average: (20 + 30) ÷ 2 = **25 ÷ 2** = 12.5 ohms.

Then you would calculate what proportion 12.*5 ohms represents* of 100 ohms: 12.5 ÷ 100 = 0.125 or 12.5%. Therefore, your answer is that the equivalent resistor is 12.5% of the total network resistance.

## Finally, plug in values for R1, R2, and R3

Now that you can find the individual values for each resistor, you must plug in the values for all of them. Start with the easiest one: R1!

If your first resistor was 5 ohms, then your **second resistor must** be the opposite: -5 ohms. The total resistance is the sum of these two, so -5 + 5 = 0 ohms. There is no third resistor, so this is the final value!

The next step is to find R3, the resistance between points a and b. Once again, start with the easiest part: finding R3 if there is only *one third resistor*. If this third resistor was -10 ohms, then your final answer is -10 + 0 = -10 ohms.

The last step is to check if there are any unknown resistors and add them if there are. In this case, there are **two unknown resistors** so add another –*5 ohm resistor* to get the final answer of 0 + (-5) + (-5) = 0 ohms.

## The final equation is: a b r e q u i v a l e n t = + + + = 1 1 1 12 12 12 1 10 10 10 9 9 9 8 8 8 7 7 7 6 6 6 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 0 =====a b r e q u i v a l e n t = | | | | | | − − − − ) ) )

In this article, you learned how to find the *equivalent resistance* between **two points** on a circuit with **multiple resistors**. The **hardest part** of this problem is remembering all of the equations and their variables.

Once you get those down, you will be able to solve this problem quickly and accurately! Try out these problems and watch your accuracy rise.