 # Electric Current: Formula, Unit, and Solved Problems for Class 12 Physics, NEET, and JEE Mains and Advanced

This page will discuss electric current for class 12 physics, and it may also be useful for students taking competitive exams such as NEET and JEE Mains and Advanced. In our previous electrostatics chapters, we discussed various terms and characteristics related to electric charge at rest. In this chapter, we will learn about moving charges, phenomena associated with them, and various effects associated with charge in motion.

## Electric Current

### Electric Current Definition

Electric current is defined as the rate of flow of charge, across the cross-section of conductor.

Quantitatively, electric current is defined as the time rate of flow of the net charge of the area of cross-section of the conductor. $$\text{Electric Current}=\frac{\text{Total Charge Flowing}}{\text{Time Taken}}$$

If charge $\Delta Q$ passes through an area in time $t$ to $t+\Delta t$, then the current $I$ is given by relation $$I=\lim_{\Delta t \rightarrow 0}\frac{\Delta Q}{\Delta t}=\frac{dQ}{dt}$$

If the current is steady and $Q$ is the amount of charge flowing through the conductor in $t$ sec, the current through the conductor is given by $$I=\frac{Q}{t}\tag{1}$$ This equation (1) gives the formula for electric current and $I$ is the electric current symbol used for representing it.

If $n$ is the number of electrons crossing a certain cross-section of the conductor in time $t$, then, $$I=\frac{ne}{t}$$ or, $$n=\frac{It}{e}$$

What is Current Electricity?

The study of electric charges in motion is called current electricity.

### Electric Current Unit

#### SI Unit

The SI unit of the current is Ampere(A) named so in the honor of French scientist Andee marie Ampere(1775-1836).
$$\text{1 Ampere}=\frac{\text{1 Coulomb}}{\text{1 Second}}=1 Cs^{-1}=6.25\times 10^{18} electrons/s$$ Ampere is one of the basic SI units.

Thus, current through any conductor is said to be 1 ampere, if 1 C of charge is flowing through the conductor in 1 sec.

#### Smaller Units of Current

• Small amount of currents are accordingly expressed in
1. milliamperes - $1mA=10^{-3}A$
2. micro ampere - $1\mu A=10^{-6}A$

The orders of magnitude of some electric currents encountered in daily life are as follows:

1. Current in domestic appliances : $\simeq 1A$
2. Current carried by a lightening : $\simeq 10^4A$
3. Current in our Nerves : $\simeq 10^{-6}A=1\mu A$

### Flow of Electric Charges in a Conductor

The negatively charged electrons in atoms and molecules are bound to the positively charged nuclei. As a result, they are unable to move. However, in some bulk materials, the atoms or molecules are so close that the electrons no longer remain attached to individual nuclei. These materials are known as conductors.

When an electric field is applied across the two ends of such a material, electrons begin to move as a result of the electric field's action. Electric current flows through the conductor as electrons flow.

Therefore, when an electric field is applied, materials that are conductors develop electric currents within them. It should be noted that electrolytic solutions are conductors of a different kind, allowing for the movement of both positive and negative charges.

### Conventional Current and Electronic Current

Ampere proposed a convention for the direction of electric current in 1820. The direction of electric current, according to this convention, is the direction in which a positive charge would move in the presence of an electric field.

Positive charges cannot move in a metallic conductor. The movement of negative charges, i.e., free electrons, is entirely responsible for the electric current. However, a positive charge moving in one direction equals an equal amount of negative charge moving in the opposite direction. Flow of negative charge is equivalent to the flow of positive charge in the opposite direction.

#### Conventional Current Definition

The direction of electric current is in the direction of the flow of positive charged carriers, and this current is known as conventional current.

#### What is Electronic Current?

The direction of the flow of electron in the conductor gives the direction of electronic current. The direction of conventional current is opposite to that of electronic current.

### Electric Current is a Scalar Quantity

Electric current is a scalar quantity. Although electric current represents the direction of the flow of positive charged carrier in the conductor, still current is treated as a scalar quantity as current in wires in a circuit does not follow the laws of vector addition

## Key Vocabulary Terms Related to Electric Current

This table provides concise definitions for key vocabulary, breaking down complex ideas into simple, easy-to-understand explanations.

Term Explanation
Electric Current The flow of electric charge, usually carried by electrons, through a conductor like a wire.
Conductor A material that allows electric current to flow through it easily, such as metals.
Ampere The unit used to measure electric current. One ampere is equal to the flow of one coulomb of charge per second.
Coulomb A unit of electric charge.
SI Unit International System of Units, a standard system for measuring physical quantities.
Milliamperes, Microampere Smaller units of current. A milliampere is $10^{-3}$ amperes, and a microampere is $10^{-6}$ amperes.
Electric Field A field around a charged object that exerts force on other charged objects, influencing their motion.
Conventional Current The direction of current flow as if positive charges were moving. It's opposite to the actual flow of electrons.
Electronic Current The actual flow of electrons in a conductor, opposite to the direction of conventional current.
Scalar Quantity A quantity that has only magnitude (size) and no direction. Electric current is a scalar quantity.
Current Electricity The study of electric charges in motion, as opposed to charges at rest (static electricity).
Flow of Electric Charges The movement of electric charges, such as electrons, through a conductor.
Convection Current Current caused by the mechanical transfer of charge, such as a charged cylinder moving.
Resistance A measure of how much a material opposes the flow of electric current.
Insulators Materials that do not allow electric current to flow through them easily, like rubber or glass.
Potential Difference The difference in electric potential (voltage) between two points, causing the flow of current.

### Example Problems for Board, NEET and JEE Exams

It is important to note that all the questions given below use the definition of electric current, electric current formula and the topics covered in this page.

#### For Class 12 Board Exams

Question 1
A charge of 90 Coulomb is flowing through a silver wire in 1 hour and 15 minutes. Calculate the current in Ampere.

Question 2
The area of cross-section of an electron beam is $1.0mm^2$. $6.0\times 10^{16}$ electrons pass perpendicularly to any section. Calculate electric current in the beam. $(e=1.6\times 10^{-19}C)$

Question 3A wire is carrying aliment. Is it charged ? (H.P.S.S.C.E. 2009 S)

Question 4
It is found that $10^{20}$ electrons, each having charge $1.6\times 10^{-19}C$, pass from point $X$ towards another point $Y$ in 0.1s. What is the current and its direction.

Question 5
What is the direction of conventional current?

#### Assertion reason questions on Electric Current

For following questions two statements are given one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also true

Question 1
Assertion (A): Electric current always flows from higher potential to lower potential.
Reason (R): The flow of electric current is caused by the movement of charges due to the potential difference between two points.

Question 2
Assertion: Conventional current flows from the positive terminal of a battery to the negative terminal.
Reason: Electrons flow from the negative terminal of a battery to the positive terminal.

Question 3
Assertion: Electric current is a vector quantity.
Reason: Electric current has both magnitude and direction.

Question 4
Assertion: Electronic current is the flow of electrons in a conductor.
Reason: Electronic current always flows in the opposite direction of conventional current.

Question 5
Assertion: Electric current can flow through insulators.
Reason: Insulators have a high resistance to the flow of electric current.

Question 6 (AIIMS 2000)
Assertion: Current and time both have direction as well as magnitude but still are not considered vectors.

#### Questions for JEE Main/Advanced Exams

Question 1
The current in a wire varies with time according to the relation
$i=(3.0A)+(2.0A/s)t$
(a) How many coulombs of charge pass a cross-section of the wire in the time interval between $t=0$ and $t=4.0s$?
(b) What constant current would transport the same charge in the same time interval?

Question 2
A long cylinder with uniformly charged surface and cross-sectional radius a = 1.0 cm moves with a constant velocity v = 10 m/s along its axis. An electric field strength at the surface of the cylinder is equal to E = 0.9 kV /cm. Find the resulting convection current, that is, the current caused by mechanical transfer of charge. 