How To Solve Power In Parallel Circuit

How to Solve Power in a Parallel Circuit

In a parallel circuit, the current is the same through each branch, but the voltage is different. The total power dissipated in a parallel circuit is equal to the sum of the power dissipated in each branch. To solve for power in a parallel circuit, you can use the following formula: ``` P = I^2R ``` where: * P is the power in watts * I is the current in amps * R is the resistance in ohms For example, if a parallel circuit has a current of 2 amps and a resistance of 4 ohms, the total power dissipated in the circuit is: ``` P = (2)^2 * 4 = 16 watts ``` You can also solve for the power in a parallel circuit using the following formula: ``` P = V^2/R ``` where: * P is the power in watts * V is the voltage in volts * R is the resistance in ohms For example, if a parallel circuit has a voltage of 12 volts and a resistance of 4 ohms, the total power dissipated in the circuit is: ``` P = (12)^2 / 4 = 36 watts ``` ## Steps to Solve Power in a Parallel Circuit To solve for power in a parallel circuit, follow these steps: 1. Identify the current in each branch of the circuit. 2. Identify the voltage across each branch of the circuit. 3. Use the formula P = I^2R to calculate the power dissipated in each branch of the circuit. 4. Add the power dissipated in each branch to find the total power dissipated in the circuit. ## Example Problem A parallel circuit has three branches, each with a resistance of 4 ohms. The current in each branch is 2 amps. What is the total power dissipated in the circuit?

Solution:

1. The current in each branch is 2 amps, so the total current in the circuit is 2 amps + 2 amps + 2 amps = 6 amps. 2. The voltage across each branch is 12 volts, so the total voltage across the circuit is 12 volts + 12 volts + 12 volts = 36 volts. 3. The power dissipated in each branch is P = I^2R = (2)^2 * 4 = 16 watts. 4. The total power dissipated in the circuit is 16 watts + 16 watts + 16 watts = 48 watts. ## Conclusion Solving for power in a parallel circuit is a simple process that can be done using the formulas P = I^2R and P = V^2/R. By following the steps outlined in this article, you can easily calculate the total power dissipated in any parallel circuit.


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