Series Circuits

Three Laws for Series Circuits

There are three fundamental relationships concerning resistance, current, and voltage for all series circuits. It is important that you learn the three fundamental laws for series circuits.

Resistance

Whenever individual resistances are connected in series, they have the same effect as one large combined resistance. Since there is only one path for current flow in a series circuit, and since each of the resistors is in line to act as an opposition to this current flow, the overall resistance is the combined opposition of all the in-line resistors.

The total resistance of a series circuit is equal to the sum of all the individual resistances in the circuit.

Rt = R1 + R2 + R3…

Using this formula, you find that the total resistance of the circuit is:

RT = 15 Ω + 5 Ω + 20 Ω = 40 Ω

Current

Since there is only one path for electron flow in a series circuit, the current is the same magnitude at any point in the circuit.

The total current in a series circuit is the same as the current through any resistance of the circuit.

IT = I1 = I2 = I3…

Given 120 V as the total voltage, and having determined the total resistance of the circuit as 40 Ω, you can now apply Ohms law to determine the total current in this circuit:

IT = 120 V/ 40 Ω = 3 A

This total circuit current would remain the same through all the individual circuit resistors.

Voltage

Before any current will flow through a resistance, a potential difference, or voltage, must be available. When resistors are connected in series, they must “share” the total voltage of the source.

The total voltage in a series circuit is equal to the sum of all the individual voltage drops in the circuit.

As current passes through each resistor in a series circuit, it establishes a difference in potential across each individual resistance.  This is commonly called voltage drop, and its magnitude is in direct proportion to the value of resistance. The greater the value of resistance, the higher the voltage drop across that resistor.

ET = E1 + E2 + E3…

Using Ohms law you can determine the voltage across each resistor.

3 A × 15 Ω = 45 V

3 A × 5 Ω = 15 V

3 A × 20 Ω = 60 V

The total source voltage is equal to the sum of the individual voltage drops:

45 V + 15 V + 60 V = 120 V

An Open in a Series Circuit

If an open is introduced, current through the circuit is interrupted. If there is no current flow, the voltage drop across each of the resistive elements is zero. However, the potential difference of the source appears across the open. If a voltmeter is connected across the open, the reading is the same as if it were connected directly across the terminals of the supply source.

Effects of Line Drop and Line Loss

Copper and aluminum are used as conductors because they offer little opposition to the flow of current. Although the resistance is often neglected in simple circuit analysis, it may be necessary to consider the resistance of lines in practical applications.

Line Drop

As the 10 A current flows through each line resistance of 0.15Ω, a small voltage drop appears across each line. This voltage drop across the line conductors is commonly referred to as a line drop.

Since there are two lines, the total drop is 2 × 1.5 V = 3 V. The net voltage across the load (117 V) is less than the source voltage.

In some situations, it may be necessary to used larger conductors, which have lower resistance, so that the line drop does not reduce the load voltage too significantly.

Line Loss

Another term associated with conductors is line loss. This is a power loss expressed in watts and is related to heat energy dissipation as current flows through the resistance of the line conductors. Line loss is calculated by using one of the power equations.

Using the previous example:

P = I² × R

P = (10A)² × 0.3Ω

P = 30 watts

*Remember:

• Line drop is expressed in volts.
• Line loss is expressed in watts.

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