# How To Work Out Total Power In A Parallel Circuit

When it comes to electrical circuits, there are two main types: series and parallel. In a series circuit, the current flows through each component in a single path. In a parallel circuit, the current can flow through multiple paths.

In this article, we will discuss how to work out the total power in a parallel circuit. We will start by looking at the formula for power in a parallel circuit, and then we will work through a few examples.

The formula for power in a parallel circuit is:

``` P = V^2 / R ```

where P is the power in watts, V is the voltage in volts, and R is the resistance in ohms.

To work out the total power in a parallel circuit, we simply add up the power dissipated by each individual resistor. For example, if we have two resistors in parallel with resistances of R1 and R2, the total power dissipated will be:

``` P = P1 + P2 = (V^2 / R1) + (V^2 / R2) ```

Let's look at a few examples to see how this works.

### Example 1

We have two resistors in parallel with resistances of 2 ohms and 4 ohms. The voltage across the resistors is 12 volts. What is the total power dissipated?

To solve this problem, we first need to find the current flowing through each resistor. The current flowing through a resistor is given by the formula:

``` I = V / R ```

So, the current flowing through the 2-ohm resistor is:

``` I1 = 12 V / 2 ohms = 6 A ```

And the current flowing through the 4-ohm resistor is:

``` I2 = 12 V / 4 ohms = 3 A ```

Now that we know the current flowing through each resistor, we can find the total power dissipated. The total power dissipated is:

``` P = P1 + P2 = (6 A)^2 * 2 ohms + (3 A)^2 * 4 ohms = 108 watts ```

### Example 2

We have three resistors in parallel with resistances of 1 ohm, 2 ohms, and 4 ohms. The voltage across the resistors is 12 volts. What is the total power dissipated?

To solve this problem, we first need to find the equivalent resistance of the parallel circuit. The equivalent resistance of a parallel circuit is given by the formula:

``` 1 / R = 1 / R1 + 1 / R2 + 1 / R3 ```

So, the equivalent resistance of the circuit in this example is:

``` 1 / R = 1 / 1 ohm + 1 / 2 ohms + 1 / 4 ohms = 7 / 12 ohms ```

Now that we know the equivalent resistance, we can find the current flowing through the circuit. The current flowing through a parallel circuit is given by the formula:

``` I = V / R ```

So, the current flowing through the circuit in this example is:

``` I = 12 V / 7 / 12 ohms = 16 A ```

Now that we know the current flowing through the circuit, we can find the total power dissipated. The total power dissipated is:

``` P = I^2 * R = (16 A)^2 * 7 / 12 ohms = 208 watts ```

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