Resistors in Series and Parallel

Electric circuits with only a single path for electricity to flow along are called series circuits. Electric circuits with multiple pathways for electricity to flow along are called parallel circuits. A circuit’s total resistance to the flow of electricity is calculated differently for series circuits than it is for parallel circuits.

If various objects are arranged to form a single conducting path between the terminals of a source of electric current, the objects are said to be connected in series. The electron current first passes from the negative terminal of the source into the first object, then flows through the other objects one after another, and finally returns to the positive terminal of the source. The current is the same throughout the circuit. In the example of the light bulb, the wires, bulb, switch, and fuse are connected in series.

When objects are connected in series, the electric current flows through them against the resistance of the first object, then against the resistance of the next object, and so on. Therefore the total resistance to the current is equal to the sum of the individual resistances. If three objects with resistances R₁, R₂, and R₃ are connected in series, their total resistance is R₁ + R₂ + R₃. For example, if a motor with a resistance of 48 ohms is connected to the terminals of a current source by two wires, each with a resistance of 1 ohm, the total resistance of the motor and wires is 48 + 1 + 1 = 50 ohms. If the voltage is 100 volts, a current of 100/50 = 2 amp will flow through the circuit.

Voltage can be thought of as being used up by the objects in a circuit. The voltage that each object uses up is called the voltage drop across that object. Voltage drop can be calculated from the equation V = IR, where V is the voltage drop across the object, I is the amount of current, and R is the resistance of the object.

In the example of the motor, the voltage drop in each wire is V = IR = 2 × 1 = 2 volts, and the voltage drop in the motor is 2 × 48 = 96 volts. Adding up the voltage drops (2 + 2 + 96) gives a total drop of 100 volts. In a series circuit the sum of the voltage drops across the objects always equals the total voltage supplied by the source.

Parallel Circuits

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.

Date: 2016-04-22; view: 1168