# Equation For Power Parallel Circuits In Series

## Equation for Power in Parallel Circuits in Series

In a parallel circuit, the current is the same through each branch, but the voltage is different. The total power dissipated in a parallel circuit is equal to the sum of the power dissipated in each branch. The equation for power in a parallel circuit is given by: ``` P = I^2R ``` where: *

### P

is the power in watts *

### I

is the current in amps *

### R

is the resistance in ohms The total current in a parallel circuit can be found using the equation: ``` I = I1 + I2 + I3 + ... ``` where: *

### I

is the total current in amps *

,

,

### I3

, ... are the currents in each branch in amps The total resistance in a parallel circuit can be found using the equation: ``` 1/R = 1/R1 + 1/R2 + 1/R3 + ... ``` where: *

### R

is the total resistance in ohms *

,

,

### R3

, ... are the resistances in each branch in ohms ## Example Let's say we have a parallel circuit with three resistors, each with a resistance of 10 ohms. The total resistance of the circuit is: ``` 1/R = 1/10 + 1/10 + 1/10 = 3/10 R = 10/3 ohms ``` The total current in the circuit is: ``` I = I1 + I2 + I3 = 10 amps + 10 amps + 10 amps = 30 amps ``` The total power dissipated in the circuit is: ``` P = I^2R = (30 amps)^2 * (10/3 ohms) = 3000 watts ``` ## Conclusion The equation for power in a parallel circuit is given by: ``` P = I^2R ``` where: *

### P

is the power in watts *

### I

is the current in amps *

### R

is the resistance in ohms The total current in a parallel circuit can be found using the equation: ``` I = I1 + I2 + I3 + ... ``` where: *

### I

is the total current in amps *

,

,

### I3

, ... are the currents in each branch in amps The total resistance in a parallel circuit can be found using the equation: ``` 1/R = 1/R1 + 1/R2 + 1/R3 + ... ``` where: *

### R

is the total resistance in ohms *

,

,

### R3

, ... are the resistances in each branch in ohms

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