How To Calculate Power In Parallel Circuit

How to Calculate Power in a 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 total power dissipated in a parallel circuit is equal to the sum of the powers dissipated by each resistor. To calculate the power dissipated by a resistor in a parallel circuit, you can use the following formula: ``` P = I^2R ``` where: * P is the power in watts * I is the current in amps * R is the resistance in ohms To calculate the total power dissipated in a parallel circuit, you can use the following formula: ``` P = Σ(I^2R) ``` where: * P is the total power in watts * I is the current in amps through each resistor * R is the resistance in ohms of each resistor ## Example 1 A parallel circuit has three resistors connected to a 12-volt battery. The resistors have resistances of 2 ohms, 4 ohms, and 6 ohms. To calculate the current through each resistor, we can use the following formula: ``` I = V/R ``` where: * I is the current in amps * V is the voltage in volts * R is the resistance in ohms For the 2-ohm resistor, the current is: ``` I = 12 V / 2 Ω = 6 A ``` For the 4-ohm resistor, the current is: ``` I = 12 V / 4 Ω = 3 A ``` For the 6-ohm resistor, the current is: ``` I = 12 V / 6 Ω = 2 A ``` To calculate the total current in the circuit, we add the currents through each resistor: ``` I = 6 A + 3 A + 2 A = 11 A ``` To calculate the power dissipated by each resistor, we can use the following formula: ``` P = I^2R ``` For the 2-ohm resistor, the power is: ``` P = (6 A)^2 * 2 Ω = 72 W ``` For the 4-ohm resistor, the power is: ``` P = (3 A)^2 * 4 Ω = 36 W ``` For the 6-ohm resistor, the power is: ``` P = (2 A)^2 * 6 Ω = 24 W ``` To calculate the total power dissipated in the circuit, we add the powers dissipated by each resistor: ``` P = 72 W + 36 W + 24 W = 132 W ``` ## Example 2 A parallel circuit has four resistors connected to a 12-volt battery. The resistors have resistances of 1 ohm, 2 ohms, 4 ohms, and 8 ohms. To calculate the current through each resistor, we can use the following formula: ``` I = V/R ``` where: * I is the current in amps * V is the voltage in volts * R is the resistance in ohms For the 1-ohm resistor, the current is: ``` I = 12 V / 1 Ω = 12 A ``` For the 2-ohm resistor, the current is: ``` I = 12 V / 2 Ω = 6 A ``` For the 4-ohm resistor, the current is: ``` I = 12 V / 4 Ω = 3 A ``` For the 8-ohm resistor, the current is: ``` I = 12 V / 8 Ω = 1.5 A ``` To calculate the total current in the circuit, we add the currents through each resistor: ``` I = 12 A + 6 A + 3 A + 1.5 A = 22.5 A ``` To calculate the power dissipated by each resistor, we can use the following formula: ``` P = I^2R ``` For the 1-ohm resistor, the power is: ``` P = (12 A)^2 * 1 Ω = 144 W ``` For the 2-ohm resistor, the power is:

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