How To Find Total Power In A Parallel Circuit

How to Find Total Power in a Parallel Circuit

In a parallel circuit, the total power dissipated is equal to the sum of the powers dissipated in each individual resistor. This can be expressed mathematically as follows: ``` Ptotal = P1 + P2 + P3 + ... + Pn ``` where: * Ptotal is the total power dissipated in the circuit, in watts * P1, P2, P3, ..., Pn are the powers dissipated in each individual resistor, in watts To find the total power in a parallel circuit, you can simply add up the powers dissipated in each resistor. For example, if a circuit has three resistors with powers of 10 watts, 20 watts, and 30 watts, respectively, the total power dissipated in the circuit would be 60 watts. You can also find the total power in a parallel circuit using the following formula: ``` Ptotal = V^2 / Rtotal ``` where: * V is the voltage across the circuit, in volts * Rtotal is the total resistance of the circuit, in ohms To find the total resistance of a parallel circuit, you can simply add up the reciprocals of the individual resistances. For example, if a circuit has three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms, respectively, the total resistance of the circuit would be 6 ohms. Once you know the total resistance of the circuit, you can plug it into the formula above to find the total power dissipated.

Example

Let's say we have a parallel circuit with three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms. The voltage across the circuit is 120 volts. We can find the total resistance of the circuit by adding up the reciprocals of the individual resistances: ``` 1 / Rtotal = 1 / 10 + 1 / 20 + 1 / 30 Rtotal = 6 ohms ``` Now we can plug this value into the formula for total power to find the total power dissipated in the circuit: ``` Ptotal = V^2 / Rtotal Ptotal = (120^2) / 6 = 2400 watts ``` Therefore, the total power dissipated in the circuit is 2400 watts.

Conclusion

Finding the total power in a parallel circuit is a simple matter of adding up the powers dissipated in each individual resistor or using the formula for total power. This information can be useful for determining the safe operating limits of a circuit or for designing a circuit to meet specific power requirements.


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