Introduction

Science and technology incorporate some ideas and techniques of their own to understand a system skilfully and easily. These techniques are called conventions. For example: Sign conventions of mirrors are used to understand the phenomenon of reflection and refraction in an easier way. 

Similarly, electric circuits sometimes become critical to analyze, therefore sign conventions of electric circuits are used to analyze them. Sign conventions applied in an electrical circuit help us to understand the state of the components of the circuit. It is helpful to get answers to questions like, whether power is delivered to or taken from the circuit. The direction of flow of current, the amount of current flowing in different branches of the circuit etc.. It standardizes the directions of the current, voltage and power in the circuits. These conventions are internationally recognized, so that professionals throughout the world can understand every project world-wide. 

Sign Convention

Based on the arrangements of the battery and components of the circuit like resistance, capacitances etc the sign conventions can be applied.

Sign conventions for the current

The current is defined as the flow of charges per unit time in a particular direction. As it is known that charges are of two types positive and negative, by convention the direction of positive current is standardized, to be the direction opposite to the flow of electrons. Thus, in all the electrical circuits the direction of the current is always opposite to the direction of electrons. 

In a battery electrons flow from the negative terminal (which is shown by the smaller bar in the sign of the battery) towards the positive terminal (which is shown by the larger bar in the sign of the battery). Thus, the direction of the current is always from the positive terminal to the negative terminal (as shown in the figure). 

Flow of electrons can also be understood as the flow of negative current. Hence, the positive current flows from the positive terminal and negative current flows from the negative current. 

Sign conventions for potential

The current in a circuit flows due to a potential difference between two points. In reference to the potentials, the current flows from higher potential to the lower potential. Thus, by sign convention the potential of the points at which the current is flowing is always less than the point from where the current is flowing. From the figure itself it can be seen that the plus (+) sign on the left of the resistances show the higher potential and the minus (-) sign on the right of the resistance show the lower potential.

Thus, for positive current flow the potential, when observed after the resistance, it comes out to be lesser in comparison to before. Therefore, a voltage drop is experienced when current flows from one point of resistance to the other. 

Sign conventions of the power

Power through the resistances in a circuit is defined as the product of the voltage, and the current flowing through the resistance.  Depending upon the sign convention used the power can be dissipative or can be generated in the circuit.

$$P=VI$$

In standard sign conventions power dissipation is given by the positive sign and the power generation is given by the negative sign. The direction of the current determines the state of the power in a circuit.

For the positive current, the power becomes positive thus it represents dissipative nature and for the negative current it becomes negative thus represents generative nature.

Related Concepts

Kirchoff’s current and voltage law are applicable on a circuit only when the direction of the current and sign conventions is set. The two laws are stated as

Kirchoff’s Current Law

The current entering a junction is equal to the current exiting the junction, leaving the junction at zero current. This can also be expressed as the equal amount of positive and negative current enters a junction (depending upon the applied sign convention).

This is completely valid to understand the mechanism of electric circuits, but can only be applied effectively when there is a standard convention analysing the flow of currents in the circuit.

Kirchoff’s Voltage Law

This law states that the summation of all potential drops inside closed loop of a circuit is always equal to zero. 

Sign conventions are very helpful in applying this law. Without pre-setting the direction of the current in the concerned circuit it is impossible to understand whether the potential drop is negative or positive along a given component of the circuit. The direction of flowing current can only determine the status of potential at a point, therefore the potential difference between two points.

Importance of Sign Convention

The need to study and understand the electricity is very important due to our increasing dependency of electronic gadgets. Sign conventions are important to understand the flow of charges, even is a highly complex circuit. It helps us to use our knowledge about the circuits to create new gadgets cheaper and more effective. More concise a gadget is, more comfortable we are with it. Today we have smart phones that are multifunctional. They can be used for calling, chatting, as a camera, a music player what not. Computers are getting smaller and smaller by day. This all is accomplished by the advancement in understanding the circuits and mediating the flow of charges.

It explains if the power is entering or exiting a circuit, hence whether it is acting as a dissipator or generator. Highly advanced labs use technologies to conduct experiments far beyond imagination of a common man, using apparatus like cyclotrons, radiation detectors and what not. Sign conventions are used in the computations of the observations that are carried to make sense from the raw data. I would not be bragging if one says that advancement is electric circuits start from the convention.

Problem:

Problem 1) Three wires which are perpendicular to each other form a junction. 3 A of current is coming into the junction from first wire, -5 A of current is coming from the second wire. What is the current in the third wire? Is it coming in or going out?

Ans: Consider the current coming into the junction as positive and the current going out of the junction as negative. Thus, negative current coming into the circuit can be interpreted as the positive current going out of the circuit. According to the Kirchoff’s current law the net current coming into the circuit is equal to the net current flowing out of the circuit.  The formula used is

$\sum I=0$

There are current through three wires. Substitute the values of current as 2 A and -5 A into the formula to calculate the current in the third wire.

$I_3+2\text{ A+(}-\text{5A)}=\text{0}$

$I_3=3\text{A}$

The positive sign show that current is going into the junction.

Context and applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• Bachelors in Science Physics
• Bachelors in Engineering
• Masters in Science Physics
• Bachelors of Technology (Electrical Engineering)
• Masters of Technology (Electrical Engineering)