# Formula For Finding Power In Parallel Circuit

## Formula for Finding Power in a Parallel Circuit

In a parallel circuit, the total current is the sum of the currents in each branch. The total voltage is the same across all branches. The power dissipated in each resistor is equal to the square of the current flowing through the resistor multiplied by the resistance of the resistor. The formula for finding the power in a parallel circuit is: ``` P = I^2R ``` where: * P is the power in watts * I is the current in amps * R is the resistance in ohms To use this formula, you need to know the current in each branch of the circuit and the resistance of each resistor. You can find the current in each branch by using Ohm's law: ``` I = V/R ``` where: * I is the current in amps * V is the voltage in volts * R is the resistance in ohms Once you know the current in each branch, you can find the total current by adding the currents in each branch. To find the resistance of each resistor, you can use the following formula: ``` R = V/I ``` where: * R is the resistance in ohms * V is the voltage in volts * I is the current in amps Once you know the total current and the resistance of each resistor, you can use the formula for finding the power in a parallel circuit to find the power dissipated in each resistor. Here is an example of how to use the formula for finding the power in a parallel circuit. A parallel circuit has two resistors, R1 = 10 ohms and R2 = 20 ohms. The voltage across the circuit is 12 volts. To find the total current, we use Ohm's law: ``` I = V/R ``` ``` I = 12 V / 30 ohms = 0.4 amps ``` To find the power dissipated in each resistor, we use the formula for finding the power in a parallel circuit: ``` P = I^2R ``` ``` P1 = (0.4 amps)^2 * 10 ohms = 1.6 watts ``` ``` P2 = (0.4 amps)^2 * 20 ohms = 3.2 watts ``` So, the total power dissipated in the circuit is 1.6 watts + 3.2 watts = 4.8 watts. ## Conclusion The formula for finding the power in a parallel circuit is: ``` P = I^2R ``` where: * P is the power in watts * I is the current in amps * R is the resistance in ohms To use this formula, you need to know the current in each branch of the circuit and the resistance of each resistor. You can find the current in each branch by using Ohm's law: ``` I = V/R ``` and the resistance of each resistor by using the formula: ``` R = V/I ``` Once you know the total current and the resistance of each resistor, you can use the formula for finding the power in a parallel circuit to find the power dissipated in each resistor.

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