# Equation For Power Parallel Circuits

## Equation for Power in Parallel Circuits

In a parallel circuit, the current is the same through each branch, but the voltage is different. The total power dissipated by the circuit is equal to the sum of the power dissipated by each branch. The equation for power in a parallel circuit is: ``` P = VI ``` where: *

### P

is the power in watts *

### V

is the voltage in volts *

### I

is the current in amps The total current in a parallel circuit can be found by adding the currents in each branch: ``` I = I1 + I2 + I3 + ... ``` The total voltage in a parallel circuit can be found by adding the voltages across each branch: ``` V = V1 + V2 + V3 + ... ``` The total resistance of a parallel circuit can be found by using the following formula: ``` 1 / R = 1 / R1 + 1 / R2 + 1 / R3 + ... ``` where: *

### R

is the total resistance in ohms *

,

,

### R3

, etc. are the resistances of the individual branches 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 = 1 / 10 + 1 / 20 + 1 / 30 = 6 / 60 = 1 / 10 ``` So, the total resistance of the circuit is 10 ohms. The total current in the circuit is: ``` I = V / R = 120 V / 10 ohms = 12 amps ``` The power dissipated by each resistor is: ``` P1 = I1^2R1 = (12 amps)^2 * 10 ohms = 1440 watts P2 = I2^2R2 = (12 amps)^2 * 20 ohms = 2880 watts P3 = I3^2R3 = (12 amps)^2 * 30 ohms = 4320 watts ``` So, the total power dissipated by the circuit is: ``` P = P1 + P2 + P3 = 1440 watts + 2880 watts + 4320 watts = 8640 watts ``` ## Conclusion The equation for power in a parallel circuit is: ``` P = VI ``` where: *

### P

is the power in watts *

### V

is the voltage in volts *

### I

is the current in amps The total current in a parallel circuit can be found by adding the currents in each branch: ``` I = I1 + I2 + I3 + ... ``` The total voltage in a parallel circuit can be found by adding the voltages across each branch: ``` V = V1 + V2 + V3 + ... ``` The total resistance of a parallel circuit can be found by using the following formula: ``` 1 / R = 1 / R1 + 1 / R2 + 1 / R3 + ... ```

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