# Electric Circuit Diagrams: Applications & Examples

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Electric circuit diagrams show you how to connect the parts of a circuit, but they also can do a lot more! In this lesson, learn how to use a circuit diagram to calculate the current in different branches of a circuit.

## What Good is a Circuit Diagram?

What happens inside a light bulb to make it light up? If you could look inside the filament of the bulb, you would see billions of tiny charged particles called electrons moving through the bulb. As they pass through, some of their energy is transformed into other forms, like light! What makes the electrons move? What gives them energy?

The energy needed to make the electrons move can be provided by a battery or by connecting the circuit to an electrical outlet in a building. All the circuits that we will examine in this lesson will use a battery as an energy source. A chemical reaction inside the battery creates a difference in electric potential between the two terminals of the battery, and this potential difference, also known as voltage, is what give the electrons energy to move through the circuit. Voltage is measured in units of Volts (V).

The rate at which electrons flow in a circuit is known as electric current, and it is measured in units of Amperes (A). Any circuit component that transforms electrical energy into other forms, including a light bulb, is known as a resistor, because it resists the flow of electrons through it. The resistance of a resistor is measured in units of Ohms.

Electric circuit diagrams use symbols to represent the parts of a circuit. They show you how to connect the circuit and make it work and can also be used to determine the current in different parts of the circuit.

## Ohm's Law

Imagine that you had a simple circuit, with one battery connected to one light bulb. What would happen if you doubled the voltage by adding a second battery? The light would probably be about twice as bright, right? The light would look brighter because the current passing through it would increase when the voltage increased.

There is a simple relationship, known as Ohm's Law, between current, voltage, and resistance for many types of resistors. Using Ohm's Law, together with a circuit diagram, you can determine the current through any resistor in a circuit.

Ohm's Law:

## Combining Resistors in Series

It's pretty easy to understand how to use Ohm's Law to calculate the current in a circuit when you have only one resistor, but what happens if you have more than one resistor in the circuit? When you have multiple resistors, you should simplify the circuit by replacing all of the resistors with one single resistor that has the same effect as all the other resistors together. The resistance of this one single resistor is known as the equivalent resistance (Req) of the circuit.

If there are no junctions between resistors and they are all in the same branch of the circuit, then we say that the resistors are in series with each other. For resistors in series, find the equivalent resistance by simply adding the resistance of each resistor.

For example, the circuit in the diagram shown below contains three resistors in series. You can find the equivalent resistance by simply adding the resistances of each one.

Once you have an equivalent resistance, you can use Ohm's Law to find the total current in the circuit.

Since there is only one path for current to flow in a circuit like this, all three resistors must have the same current flowing through them.

## Combining Resistors in Parallel

In the diagram below, the three resistors are now connected in parallel with each other. The current in the wire coming from the battery must split three ways to pass through each parallel resistor. Unlike resistors in series, resistors in parallel do NOT have the same current through them. However, the sum of the currents passing through each resistor must equal the total current passing through the battery.

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