How To Calculate Total Resistance In A Parallel Circuit Example

How to Calculate Total Resistance in a Parallel Circuit

In a parallel circuit, the total resistance is always less than the resistance of any individual resistor. This is because the current can flow through multiple paths, and the more paths there are, the less resistance there is to the flow of current. The total resistance of a parallel circuit can be calculated using the following formula: ``` Rt = 1 / (1/R1 + 1/R2 + ... + 1/Rn) ``` Where: *

Rt

is the total resistance of the circuit *

R1

R2

, ...,

Rn

are the resistances of the individual resistors For example, if you have a parallel circuit with three resistors of 10 ohms, 20 ohms, and 30 ohms, the total resistance of the circuit would be: ``` Rt = 1 / (1/10 + 1/20 + 1/30) = 5 ohms ``` As you can see, the total resistance of the circuit is less than the resistance of any individual resistor. ## Calculating Total Resistance in a Parallel Circuit with Two Resistors In the case of a parallel circuit with two resistors, the total resistance can be calculated using the following formula: ``` Rt = R1 * R2 / (R1 + R2) ``` For example, if you have a parallel circuit with two resistors of 10 ohms and 20 ohms, the total resistance of the circuit would be: ``` Rt = 10 * 20 / (10 + 20) = 15 ohms ``` ## Calculating Total Resistance in a Parallel Circuit with Multiple Resistors If you have a parallel circuit with multiple resistors, you can calculate the total resistance using the following steps: 1. First, add the reciprocals of the resistances of the individual resistors. 2. Then, take the reciprocal of the sum of the reciprocals. For example, if you have a parallel circuit with three resistors of 10 ohms, 20 ohms, and 30 ohms, the total resistance of the circuit would be: 1. Add the reciprocals of the resistances of the individual resistors: ``` 1/10 + 1/20 + 1/30 = 6/60 ``` 2. Take the reciprocal of the sum of the reciprocals: ``` 1 / (6/60) = 10 ohms ``` As you can see, the total resistance of the circuit is less than the resistance of any individual resistor. ## Example of Calculating Total Resistance in a Parallel Circuit Let's look at an example of calculating total resistance in a parallel circuit. We have a parallel circuit with three resistors of 10 ohms, 20 ohms, and 30 ohms. We can calculate the total resistance of the circuit using the following steps: 1. Add the reciprocals of the resistances of the individual resistors: ``` 1/10 + 1/20 + 1/30 = 6/60 ``` 2. Take the reciprocal of the sum of the reciprocals: ``` 1 / (6/60) = 10 ohms ``` So, the total resistance of the circuit is 10 ohms. ## Conclusion In this article, we learned how to calculate total resistance in a parallel circuit. We also looked at an example of calculating total resistance in a parallel circuit with three resistors.

Physics For Kids Resistors In Series And Parallel