Power Formula For Parallel Circuit

In a parallel circuit, the voltage across each resistor is the same, but the current through each resistor is different. The total current in a parallel circuit is the sum of the currents through each resistor. The power dissipated by a resistor is equal to the product of the current through the resistor and the voltage across the resistor. The following formula can be used to calculate the power dissipated by a resistor in a parallel circuit: ``` P = I^2R ``` where: * P is the power in watts * I is the current in amps * R is the resistance in ohms The total power dissipated in a parallel circuit is equal to the sum of the powers dissipated by each resistor: ``` P_total = P_1 + P_2 + ... + P_n ``` where: * P_total is the total power in watts * P_1, P_2, ..., P_n are the powers dissipated by each resistor in watts To find the total resistance of a parallel circuit, you can use the following formula: ``` 1/R_total = 1/R_1 + 1/R_2 + ... + 1/R_n ``` where: * R_total is the total resistance in ohms * R_1, R_2, ..., R_n are the resistances of each resistor in ohms ## Example Consider a parallel circuit with three resistors, R1 = 10 ohms, R2 = 20 ohms, and R3 = 30 ohms. The total resistance of the circuit is: ``` 1/R_total = 1/10 + 1/20 + 1/30 = 6/60 = 1/10 ohms ``` The total current in the circuit is: ``` I = V/R_total = 10 volts/1/10 ohms = 10 amps ``` The power dissipated by each resistor is: ``` P_1 = I^2R_1 = (10 amps)^2(10 ohms) = 1000 watts P_2 = I^2R_2 = (10 amps)^2(20 ohms) = 2000 watts P_3 = I^2R_3 = (10 amps)^2(30 ohms) = 3000 watts ``` The total power dissipated in the circuit is: ``` P_total = P_1 + P_2 + P_3 = 1000 watts + 2000 watts + 3000 watts = 6000 watts ``` ## Conclusion The power formula for a parallel circuit can be used to calculate the power dissipated by each resistor in the circuit and the total power dissipated in the circuit. The total resistance of a parallel circuit can be calculated using the reciprocal of the sum of the reciprocals of the resistances of each resistor.

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