# Power Calculation In Parallel Circuit

## Power Calculation in Parallel Circuits

In a parallel circuit, the voltage across each branch is the same, but the current through each branch can be different. This is because the total current in a parallel circuit is the sum of the currents through each branch. The power dissipated in a resistor is given by the equation \$P = I^2R\$, where \$P\$ is the power in watts, \$I\$ is the current in amps, and \$R\$ is the resistance in ohms. To calculate the total power dissipated in a parallel circuit, we can use the following equation: ``` P = (V^2)/R ``` where \$P\$ is the total power in watts, \$V\$ is the voltage across the circuit in volts, and \$R\$ is the total resistance of the circuit in ohms. To calculate the power dissipated in each branch of a parallel circuit, we can use the following equation: ``` P = (V^2)/R_b ``` where \$P\$ is the power in watts, \$V\$ is the voltage across the branch in volts, and \$R_b\$ is the resistance of the branch in ohms. ### Example Consider the following parallel circuit:

The total resistance of this circuit is: ``` R = 1/(1/10 + 1/15) = 6 ohms ``` The total power dissipated in the circuit is: ``` P = (12^2)/6 = 24 watts ``` The power dissipated in each branch is: ``` P_1 = (12^2)/10 = 14.4 watts P_2 = (12^2)/15 = 9.6 watts ``` ### Summary In a parallel circuit, the total voltage across the circuit is the same as the voltage across each branch. The total current in a parallel circuit is the sum of the currents through each branch. The power dissipated in a resistor is given by the equation \$P = I^2R\$. The total power dissipated in a parallel circuit is given by the equation \$P = (V^2)/R\$. The power dissipated in each branch of a parallel circuit is given by the equation \$P = (V^2)/R_b\$.

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