Electric Current for class 12 physics, NEET, JEE Main 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

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, $$n=\frac{It}{e}$$

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.

Smaller Units of Current

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

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.

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.

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

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.

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

Solution

The current flowing in the wire is $$I=\frac{Q}{t}$$ Here $Q= 90 C$ and $t=\text{1 hour 15 minutes}=75\times 60 s$.
Therefore,
$$I=\frac{90 C}{(75\times 60 s)}=0.02A$$

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. $(e=1.6\times 10^{-19}C)$

Solution

The total charge passing per second perpendicularly to the section is $$Q=ne=(6.0\times 10^{16})\times (1.6\times 10^{-19})=9.6\times 10^{-3}C$$ The electric current $$I=\frac{Q}{t}=\frac{9.6\times 10^{-3}}{1s}=9.6\times 10^{-3}A$$ Since the charge on electron is negative, the direction of current will be opposite to the motion of electron beam.

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

Answer

No. The flow of free electrons in a conductor is referred to as electric current. The number of electrons leaving the wire at any given time is always equal to the number of electrons flowing from the battery into it. As a result, the net charge on the wire is zero.

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.

Solution

Here, $Q=ne=10^{20}\times 1.6\times 10^{-19}=16 C$ and $t=0.1s$
therefore,
$I=\frac{Q}{t}=\frac{16}{0.1}=160 A$
The direction of conventional current is from point $Y$ to $X$.

In an electric circuit, the direction of conventional current is from positive to negative terminal of the battery.

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.

Explaination

Answer: Option A
Explanation: The assertion is true, as electric current always flows from a point of higher electrical potential to a point of lower electrical potential. This is because charged particles move from a region of higher potential energy to a region of lower potential energy. The reason is also true, as the flow of electric current is indeed caused by the movement of charges due to the potential difference between two points. When there is a potential difference between two points, an electric field is established, which exerts a force on the charged particles, causing them to move from the higher potential point to the lower potential point. This movement of charges constitutes the flow of electric current.

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.

Explaination

Answer: Option B
Explanation: Both the assertion and reason are true. However, the reason is not the correct explanation of the assertion. The assertion is about conventional current, which is a flow of positive charges, while the reason is about electron flow, which is the flow of negative charges. In conventional current, we define current as the flow of positive charges from the positive terminal of the battery to the negative terminal.

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

Explaination

Answer: Option A
Explanation: The assertion is true. The reason is true, and is explaination of assertion.

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.

Explaination

Answer: Option B
Explanation: Both the assertion and reason are true, but the reason is not the correct explanation of the assertion. The assertion is correct, as electronic current does indeed refer to the flow of electrons in a conductor. The reason is also correct, but it is not an explaination of the assertion.

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

Explaination

Answer: Option C
Explanation: The assertion is false. Electric current cannot flow through insulators. The reason is true, as insulators do have a high resistance to the flow of electric current, but this does not mean that electric current can flow through them. In fact, insulators are used precisely because they prevent 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.
Reason: They do not follow laws of vector addition.

Explaination

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?
Answer

(a) \begin{align*} i=\frac{dq}{dt}\\ \int_0^q {dq}&=\int_0^4idt\\ q&=\int_0^4(3+2t)dt\\ &=[3t+t^2]_0^4 = 12+16=28C \end{align*} (b) $i=\frac{q}{t}=\frac{28}{4}=7A$

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.

Solution

Let us assume that the cylinder is uniformly charged and $\sigma$ be its surface charge density
Using Gauss's theorem, we know that the electric field on the surface of the cylinder is equal to
$\vec E=\frac{\sigma}{\epsilon_0}\hat n$
or,
$\vec E =\frac{dQ}{dA}\frac{1}{\epsilon_0} \tag{1}$
Consider an element of infinitesimal length $dx$ on the cylinder then from the equation (1) we have,
$E\cdot da=\frac{dq}{\epsilon_0}$
or,
$E\cdot2\pi a dx \cdot \epsilon_0=dq \tag{2}$
the resulting current due to the motion of the cylinder is
$$\frac{dq}{dt}=E\cdot 2\pi a \epsilon_0\frac{dx}{dt}$$ or,
$i=2\pi\epsilon_0aEv$
Putting in all the values we get
$i=2\times 3.14\times 8.85\times 10^{-12}\frac{C^2}{N.m^2}\times 1.0\times 10^{-2}m\times 90\,kV/m\times 10m/s$
calculating it we get
$i=0.5\times 10^{-6}A=0.5\mu A$

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

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