# How To Calculate The Total Power In A Parallel Circuit

In a parallel circuit, the total power is equal to the sum of the powers dissipated by each individual resistor. This can be calculated using the following formula: ``` P = ΣPi ``` where P is the total power, Pi is the power dissipated by resistor i, and i is the index of the resistor. To calculate the power dissipated by a resistor in a parallel circuit, you can use the following formula: ``` P = V2/R ``` where P is the power, V is the voltage across the resistor, and R is the resistance of the resistor. Once you know the power dissipated by each resistor, you can add them together to find the total power in the circuit. For example, consider the following parallel circuit:

This circuit consists of three resistors, R1, R2, and R3, connected in parallel. The voltage across the resistors is 12 V, and the resistances of the resistors are 10 Ω, 20 Ω, and 30 Ω, respectively. To calculate the total power in the circuit, we first need to calculate the power dissipated by each resistor. The power dissipated by R1 is: ``` P1 = (12 V)^2 / 10 Ω = 144 W ``` The power dissipated by R2 is: ``` P2 = (12 V)^2 / 20 Ω = 72 W ``` The power dissipated by R3 is: ``` P3 = (12 V)^2 / 30 Ω = 48 W ``` The total power in the circuit is: ``` P = P1 + P2 + P3 = 144 W + 72 W + 48 W = 264 W ``` Therefore, the total power in the circuit is 264 W.

In addition to the total power, you can also calculate the average power in a parallel circuit. The average power is the total power divided by the number of resistors in the circuit. In the example above, the average power is: ``` Pavg = P / 3 = 264 W / 3 = 88 W ``` The average power is often used to compare the power consumption of different circuits.

Calculating the total power in a parallel circuit is a simple process that can be easily done using the formulas provided in this article. By understanding how to calculate the total power in a parallel circuit, you can better understand the operation of parallel circuits and how they can be used to design efficient electrical systems.

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