Parallel Circuits

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If various objects are connected to form separate paths between the terminals of a source of electric current, they are said to be connected in parallel. Each separate path is called a branch of the circuit. Current from the source splits up and enters the various branches. After flowing through the separate branches, the current merges again before reentering the current source.

The total resistance of objects connected in parallel is less than that of any of the individual resistances. This is because a parallel circuit offers more than one branch (path) for the electric current, whereas a series circuit has only one path for all the current.

The electric current through a parallel circuit is distributed among the branches according to the resistances of the branches. If each branch has the same resistance, then the current in each will be equal. If the branches have different resistances, the current in each branch can be determined from the equation I = V/R, where I is the amount of current in the branch, V is the voltage, and R is the resistance of the branch.

The total resistance of a parallel circuit can be calculated from the equation


where R is the total resistance and R1, R2, ... are the resistances of the branches. For example, if a parallel circuit consists of three branches with resistances of 10, 15, and 30 ohms, then


Therefore, R = 5 ohms. In this circuit, a voltage of 150 volts would produce an electric current of I = V/R = 150/5 = 30 amp.

The greater the resistance of a given branch, the smaller the portion of the electric current flowing through that branch. If a parallel circuit of three branches, with resistances of 10, 15, and 30 ohms, is connected to a 150-volt source, the branch with a resistance of 10 ohms would receive a current of V/R = 150/10 = 15 amp. Similarly, the 15-ohm branch receives 10 amp, and the 30-ohm branch receives 5 amp. These branch currents add up to a total current of 30 amp, which is the value obtained by dividing the voltage by the total resistance.

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