#### Series Circuits - Resistance

A simplified series circuit is made up of three elements:

• a source,
• resistors, in which the electrical energy is utilized and is commonly referred to as loads,
• and ideal conductors, with no assumed resistance, to connect the elements in series.

Consider a typical household electrical outlet as a 120-volt source for the circuit and the light bulbs as resistors in a closed circuit. The wires are assumed to have no resistance themselves and connect each of the light bulbs in a single, closed circuit.

Since there is only one path for current to flow in this series circuit, the current or electron flow must be the same in each segment of the circuit. This means that the current leaving the source is equal to the amount of current through each resistance.

There are three rules governing the simple series circuits of resistive elements. They are:

1. The current flow is the same through each element of the series circuit.
2. The combined resistance of the various loads in series is the sum of the separate resistances.
3. The voltage across the source or power supply is equal to the sum of the voltage drops across the separate loads in series.

Solution:

We can now determine the current flow through and voltage drop across each element of the circuit shown. Recalling that Ohm's Law can be applied to the whole circuit or any part of the circuit, we can determine the current flow in the circuit. First calculating the total resistance using Rule 2,

Then applying Ohm's Law for the total circuit, we find

Recalling Rule 1, we know the current in each resistor is

We can find the voltage drop for each resistor by again applying Ohm's Law, this time to each of the resistors.

Note we can check our calculations by using Rule 3: