## Total Power Formula In Parallel Circuit

In a parallel circuit, the total power dissipated is equal to the sum of the powers dissipated by each individual resistor. This can be expressed mathematically as follows: ``` P_t = P_1 + P_2 + ... + P_n ``` where: *### P_t

is the total power dissipated in the circuit (in watts) *### P_1

,### P_2

, ...,### P_n

are the powers dissipated by each individual resistor (in watts) The total power dissipated in a parallel circuit can be calculated by using the following steps: 1. Find the equivalent resistance of the circuit. 2. Use the equivalent resistance to calculate the total current flowing through the circuit. 3. Use the total current and the individual resistances to calculate the power dissipated by each resistor. 4. Add the powers dissipated by each resistor to find the total power dissipated in the circuit. For example, consider the following parallel circuit: The equivalent resistance of this circuit is: ``` R_eq = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} ``` ``` R_eq = \frac{1}{10 \Omega} + \frac{1}{20 \Omega} + \frac{1}{30 \Omega} ``` ``` R_eq = 6.67 \Omega ``` The total current flowing through the circuit is: ``` I_t = \frac{V}{R_eq} ``` ``` I_t = \frac{12 V}{6.67 \Omega} ``` ``` I_t = 1.8 A ``` The power dissipated by each resistor is: ``` P_1 = I_t^2 R_1 ``` ``` P_1 = (1.8 A)^2 (10 \Omega) ``` ``` P_1 = 32.4 W ``` ``` P_2 = I_t^2 R_2 ``` ``` P_2 = (1.8 A)^2 (20 \Omega) ``` ``` P_2 = 72 W ``` ``` P_3 = I_t^2 R_3 ``` ``` P_3 = (1.8 A)^2 (30 \Omega) ``` ``` P_3 = 108 W ``` The total power dissipated in the circuit is: ``` P_t = P_1 + P_2 + P_3 ``` ``` P_t = 32.4 W + 72 W + 108 W ``` ``` P_t = 212 W ``` Therefore, the total power dissipated in the parallel circuit is 212 watts. ## Conclusion The total power formula in a parallel circuit is a simple and straightforward way to calculate the total power dissipated in a circuit. This formula can be used to calculate the total power dissipated in any parallel circuit, regardless of the number of resistors in the circuit.Power In A Parallel Circuit

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