# Power Equation For Parallel Circuit

## Power Equation For Parallel Circuit

In this article, we will discuss the power equation for a parallel circuit. We will start by defining what a parallel circuit is, and then we will derive the power equation. Finally, we will apply the power equation to a few examples. ## What is a Parallel Circuit? A parallel circuit is a circuit in which two or more components are connected in parallel. This means that the components are all connected to the same voltage source, but they are not connected to each other. In other words, the current can flow through any of the components, and it does not matter which one it takes. ## Deriving the Power Equation The power equation for a parallel circuit is given by the following formula: ``` P = I^2R ``` where P is the power in watts, I is the current in amps, and R is the resistance in ohms. To derive this equation, we start with the definition of power: ``` P = IV ``` where P is the power in watts, I is the current in amps, and V is the voltage in volts. In a parallel circuit, the voltage across all of the components is the same. This is because the components are all connected to the same voltage source. So, we can substitute V into the equation for power: ``` P = IV = I^2R ``` This is the power equation for a parallel circuit. ## Applying the Power Equation We can use the power equation to calculate the power dissipated by a parallel circuit. For example, consider the following parallel circuit: ``` [Image of a parallel circuit] ``` The circuit consists of three resistors, each with a resistance of 10 ohms. The voltage source is 12 volts. We can calculate the total current in the circuit using the following formula: ``` I = V/R ``` where I is the current in amps, V is the voltage in volts, and R is the resistance in ohms. In this case, the total current is: ``` I = 12 V / 10 ohms = 1.2 amps ``` We can then calculate the power dissipated by each resistor using the following formula: ``` P = I^2R ``` where P is the power in watts, I is the current in amps, and R is the resistance in ohms. In this case, the power dissipated by each resistor is: ``` P = (1.2 amps)^2 * 10 ohms = 14.4 watts ``` Therefore, the total power dissipated by the circuit is 14.4 watts. ## Conclusion In this article, we have discussed the power equation for a parallel circuit. We have derived the equation and applied it to a few examples. We hope that this article has helped you to understand the power equation for parallel circuits. ## References * [The Physics Classroom](https://www.physicsclassroom.com/class/circuits/Lesson-1/Power-in-Parallel-Circuits) * [Khan Academy](https://www.khanacademy.org/science/physics/electric-circuits/circuits-resistance/a/parallel-circuits-power)

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