I_total = I_1 + I_2 + I_3 + ...
where I_total is the total current in the circuit and I_1, I_2, I_3, etc. are the currents in each branch of the circuit.
The division of current in a parallel circuit is determined by the resistance of each branch. The branch with the lowest resistance will carry the most current. This can be explained using Ohm's law, which states that the current in a circuit is directly proportional to the voltage and inversely proportional to the resistance.
In a parallel circuit, the voltage across each branch is the same. Therefore, the current in each branch will be inversely proportional to the resistance of that branch.
For example, consider a parallel circuit with two branches. Branch 1 has a resistance of 10 ohms and branch 2 has a resistance of 20 ohms. If the voltage across the circuit is 12 volts, then the current in branch 1 will be:
I_1 = V/R = 12 V / 10 ohms = 1.2 A
The current in branch 2 will be:
I_2 = V/R = 12 V / 20 ohms = 0.6 A
The total current in the circuit will be:
I_total = I_1 + I_2 = 1.2 A + 0.6 A = 1.8 A
Therefore, in a parallel circuit, the current divides between the various branches of the circuit and the total current is the sum of the currents in each branch. The division of current is determined by the resistance of each branch, with the branch with the lowest resistance carrying the most current.
