How To Find The Total Power In A Parallel Circuit

How to Find the Total Power in a Parallel Circuit

In a parallel circuit, the total power is equal to the sum of the powers dissipated by each individual resistor. This can be expressed mathematically as follows: ``` P_T = \sum_{i=1}^n P_i ``` where: *

P_T

is the total power dissipated in the circuit (in watts) *

P_i

is the power dissipated by resistor

i

(in watts) *

n

is the number of resistors in the circuit To find the total power in a parallel circuit, you can use the following steps: 1. Calculate the current through each resistor using Ohm's law: ``` I_i = \frac{V}{R_i} ``` where: *

I_i

is the current through resistor

i

(in amps) *

V

is the voltage across the circuit (in volts) *

R_i

is the resistance of resistor

i

(in ohms) 2. Calculate the power dissipated by each resistor using the following formula: ``` P_i = I_i^2R_i ``` 3. Add the powers dissipated by each resistor to find the total power in the circuit. For example, consider the following parallel circuit:

This circuit has three resistors, each with a resistance of 10 ohms. The voltage across the circuit is 12 volts. To find the total power dissipated in the circuit, we first need to calculate the current through each resistor. ``` I_1 = \frac{V}{R_1} = \frac{12 V}{10 \Omega} = 1.2 A I_2 = \frac{V}{R_2} = \frac{12 V}{10 \Omega} = 1.2 A I_3 = \frac{V}{R_3} = \frac{12 V}{10 \Omega} = 1.2 A ``` Now we can calculate the power dissipated by each resistor. ``` P_1 = I_1^2R_1 = (1.2 A)^2(10 \Omega) = 14.4 W P_2 = I_2^2R_2 = (1.2 A)^2(10 \Omega) = 14.4 W P_3 = I_3^2R_3 = (1.2 A)^2(10 \Omega) = 14.4 W ``` Finally, we add the powers dissipated by each resistor to find the total power in the circuit. ``` P_T = P_1 + P_2 + P_3 = 14.4 W + 14.4 W + 14.4 W = 43.2 W ``` Therefore, the total power dissipated in this parallel circuit is 43.2 watts. ## Conclusion In this article, we have shown how to find the total power in a parallel circuit. We used Ohm's law to calculate the current through each resistor, and then we used the power equation to calculate the power dissipated by each resistor. Finally, we added the powers dissipated by each resistor to find the total power in the circuit.


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