# How To Calculate Power In Dc Parallel Circuits

## How to Calculate Power in DC Parallel Circuits

In a parallel circuit, the voltage across each resistor is the same, but the current through each resistor is different. The total current in the circuit is the sum of the currents through each resistor. The power dissipated by a resistor is equal to the square of the current through the resistor multiplied by the resistance of the resistor. $$P = I^2R$$ where: * $P$ is the power in watts * $I$ is the current in amps * $R$ is the resistance in ohms In a parallel circuit, the total power dissipated is equal to the sum of the powers dissipated by each resistor. $$P_{total} = \sum_{i=1}^n P_i$$ where: * $P_{total}$ is the total power in watts * $P_i$ is the power dissipated by resistor $i$ in watts * $n$ is the number of resistors in the circuit To calculate the power in a parallel circuit, you can use the following steps: 1. Find the total current in the circuit. 2. Find the resistance of each resistor. 3. Calculate the power dissipated by each resistor. 4. Add the powers dissipated by each resistor to find the total power in the circuit. Here is an example of how to calculate the power in a parallel circuit. A parallel circuit has three resistors: $R_1 = 2\Omega$, $R_2 = 4\Omega$, and $R_3 = 6\Omega$. The voltage across the circuit is $V = 12\volts$. To find the total current in the circuit, we use the following formula: $$I = \frac{V}{R}$$ In this case, we have: $$I = \frac{12\volts}{2\Omega + 4\Omega + 6\Omega} = 2\amps$$ To find the resistance of each resistor, we use the following formula: $$R = \frac{V}{I}$$ In this case, we have: * $R_1 = \frac{12\volts}{2\amps} = 6\Omega$ * $R_2 = \frac{12\volts}{4\amps} = 3\Omega$ * $R_3 = \frac{12\volts}{6\amps} = 2\Omega$ To calculate the power dissipated by each resistor, we use the following formula: $$P = I^2R$$ In this case, we have: * $P_1 = (2\amps)^2(6\Omega) = 24\watts$ * $P_2 = (2\amps)^2(3\Omega) = 12\watts$ * $P_3 = (2\amps)^2(2\Omega) = 8\watts$ To find the total power in the circuit, we add the powers dissipated by each resistor: $$P_{total} = 24\watts + 12\watts + 8\watts = 44\watts$$ Therefore, the total power dissipated in the circuit is 44 watts. ## Conclusion In this article, we have shown how to calculate power in a DC parallel circuit. We have used a step-by-step example to show how to find the total current in the circuit, the resistance of each resistor, and the power dissipated by each resistor. We have also shown how to find the total power in the circuit.

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