Electric Circuit Diagram Formula & Symbols | What is an Electrical Circuit? | Study.com

Circuit Diagram

A circuit diagram is a simplified drawing of an electrical circuit. It uses a solid line to show the conductor or wires that determine the path of the circuit. On the path are symbols to represent the various parts of the circuit such as the power source and resistors. These diagrams are used to design, construct, and maintain electrical circuits. They can also be used to calculate the current in different parts of the circuit.

A circuit diagram for a simple electrical circuit.

Circuit Symbols

Symbols are used to identify the various components of the electric circuit. Some common symbols are:

Power Source

A power source, or battery, often shown with two parallel vertical lines that are not connected. Sometimes the two lines will be the same length, other times one will be shorter.

The symbol for an electrical cell, such as a battery or other power source.

Resistor

A
resistor, a component that transforms electrical energy into other forms, such as a light bulb. A resistor symbol is a zig-zig line. A light bulb can have a different symbol, often a circle with a wavy line inside of it.

The symbol for a resistor.

LED Symbol

An LED symbol has also developed, which is a triangle on its side with a vertical line at its tip and two diagonal arrows above it on the right.

An LED symbol for a circuit diagram.

Series and Parallel Circuits

Two different types of circuits are series circuits and parallel circuits. Both series and parallel circuits can have multiple resistors or other features in them.

Series Electrical Circuit

In a series circuit, there is only one path for the electricity to follow. The resistors are in a series, all in a chain along the path of the circuit. The amount of current going through each resistor is the same in a series circuit. Also with a series circuit, the electricity goes to everything at once or nothing at all. It is not possible for part of the series to be receiving electricity while other parts are not. An example of this is with a string of lights. If a string of lights is set up as a series circuit, when one light bulb goes out the entire string of lights stops working.

An example of a serial circuit.

Parallel Electrical Circuit

A parallel circuit has different branches in which the electricity can flow. This is an advantage in that, if one branch of the circuit breaks, the other branches can continue working. Electricity will continue to flow along the other branches, despite any problems that may occur in one section. Household appliances are set up with parallel circuits. If one appliance in the kitchen stops working, it does not cause the rest of the appliances to also stop working.

An example of a simple parallel circuit.

Current Formula

The electric current unit that is used is Amperes or amps for short. Current is directly related to both the voltage and resistance that exists in a circuit. The relationship between these is expressed in Ohm’s Law, which is {eq}I = \frac{V}{R} {/eq}. In this equation, I is the current, V is the voltage, and R is the resistance measured in Ohms.

Ohm’s Law can be used to calculate the amount of current flowing through an electrical circuit.

Current in Circuit

In a basic circuit that has one resistor, calculating the current simply involves plugging numbers into the equation and solving. For example, to find the current through a 5 Ohm resistor in a circuit with 240 volts, simply plug in the numbers and solve:

{eq}I = \frac{240}{5} = 48 amps {/eq}

But for both series and parallel circuits, there is more involved in the process. The equivalent resistance needs to be determined. If all of the resistors were combined into one resistor that did the same thing, that would be an equivalent resistor. Its resistance is what needs to be used in Ohm’s Law.

Current in Series Circuit

For a series circuit, simply add the resistance of each resistor and use that number in the equation.

To calculate the voltage in this circuit, add all of the resistors together and solve.

For the series circuit in this example, the resistance needs to first be determined. To do so, add the resistors together to get 30. Then, plug in the numbers and solve for the missing voltage.

{eq}0.5 = \frac{V}{30} {/eq}

{eq}30 \cdot 0.5 = V {/eq}

{eq}V = 15 Volts {/eq}

Current in Parallel Circuit

With a parallel circuit, the resistors do not have the same current flowing through them, but the sum of the current flowing through all the resistors must equal the sum of the current flowing through the battery. The equivalent resistance in a parallel circuit is found by using the formula {eq}\frac{1}{R_eq} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + . . . {/eq}.

An additional step must be done with the resistors before calculating the voltage in this battery.

The parallel circuit in the image shows two resistors with 150 and 400 Ohms. To find the equivalent resistance:

{eq}\frac{1}{R_eq} = \frac{1}{150} + \frac{1}{400} {/eq}

{eq}\frac{1}{R_eq} = \frac{8}{1200} + \frac{3}{1200} {/eq}

{eq}\frac{1}{R_eq} = \frac{11}{1200} {/eq}

{eq}R_eq = \frac{1200}{11} = 109.09 Ohms {/eq}

This number can then be used in Ohm’s Law to determine the voltage.

{eq}5 = \frac{V}{109.09} {/eq}

{eq}109.09 \times 5 = 545.45 V {/eq}

Once the voltage is determined, it is possible to find the current going through each resistor, as well. The voltage through each resistor is equal to the voltage in the battery. Simply use the voltage (545.45 V) and the resistance of each resistor to calculate the current using Ohm’s Law.

Electric Circuit: Examples

Understanding Ohm’s Law and the extra steps involved in finding the equivalent resistance for series and parallel circuits is important to know. By using these formulas, solving series and parallel circuit problems can be done with relative ease. The following are a few examples of how to apply Ohm’s Law to various situations.

Series Circuit: Example

To find the current in this series circuit, first add the resistors together.

↠ What is the current in the circuit shown in the image?

First, the equivalent resistance needs to be determined. Since this is a series circuit, the resistance is added together, {eq}3 + 2 = 5 {/eq}.

Next, put the numbers into Ohm’s Law to determine the current.

{eq}I = \frac{5}{5} = 1 amp {/eq}

Parallel Circuit: Example

A parallel circuit. Using Ohms Law, the voltage can be calculated.

↠ In the parallel circuit shown, what is the equivalent resistance?

Use the equation given in the previous section.

{eq}\frac{1}{R_eq} = \frac{1}{40} + \frac{1}{100} + \frac{1}{200} {/eq}

{eq}\frac{1}{R_eq} = \frac{5}{200} + \frac{2}{200} + \frac{1}{200} = \frac{8}{200} = \frac{1}{25} {/eq}

{eq}R_eq = 25 Ohms {/eq}

{eq}\rule{8cm}{0.4pt} {/eq}

↠ Using the same circuit, what is the voltage?

Use Ohm’s Law to solve, plugging in the 25 Ohms calculated from the previous problem for the resistance.

{eq}5 = \frac{V}{25} {/eq}

{eq}25 \times 5 = 125 V {/eq}

{eq}\rule{8cm}{0.4pt} {/eq}

↠ And finally, what is the current through the 100 Ohm resistor in this same circuit?

The voltage going through the resistor is the same as the voltage in the battery, so using the 125 V and the 100 Ohm, the current can be calculated as:

{eq}I = \frac{125}{100} = 1.25 amps {/eq}

Lesson Summary

An electrical circuit is a pathway through which an electric current can flow. All electrical circuits have a power source, a load or a resistor (such as a light bulb), and conductors to carry the current. The battery provides the energy needed to make electrons flow at a rate called the current. A chemical reaction takes place creating a difference in electrical potential, called the voltage, and gives the electrons the energy to move through the circuit. A circuit diagram is a simplified drawing of an electrical circuit. Various symbols are used to identify different components. These diagrams are used to design, construct, and maintain electrical circuits. They can also be used to calculate the current in different parts of the circuit.

Current is directly related to both the voltage and resistance and the relationship between these is expressed in Ohm’s Law: {eq}I = \frac{V}{R} {/eq}. A series circuit contains all components on one path. A parallel circuit has multiple paths on which the electrons flow. The equivalent resistance needs to be determined in these types of circuits and put into Ohm’s Law. In a series circuit all of the resistors are added together. In a parallel circuit the formula {eq}\frac{1}{R_eq} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + . . . {/eq} is used to find the equivalent resistance.