Calculate the steady current through the \$2\Omega\$ resistor in the circuit shown in the figure.

Effective resistance,\${ R }_{ 12 }=\dfrac { 1 }{ 2 } +\dfrac { 1 }{ 3 } =\dfrac { 5 }{ 6 } \$ \${ R }_{ 12 }=1.2\Omega \$ resistance,\${ R }_{ 12 }\$ is in series \$2.8\Omega \$ Total resistance \$=1.2+2.8=4.0\Omega \$ Current,\$I=\dfrac { 6 }{ 4 } =1.5A\$ Potential difference,\$AB=1.5\times 1.2=1.8V\$ Current through \$2\Omega =\dfrac { 1.8 }{ 2 } =0.9A\$.

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>> $Introduction to Electric Current due to ...$

Introduction to Electric Current due to flow of Electrons per unit time

Q: A long straight wire of radius a carries a steady current \$I.\$ The current is uniformly distributed over its cross-section. The ratio o the magnetic fields \$B\$ and \$B',\$ at radial distances \$\dfrac{a}{2}\$ and \$2a\$ respectively, from the axis of the wire is

Consider two amperian loops of radius \$a/2\$ and \$2a\$ as shown in the diagram\$.\$Applying ampere's circuital law for these loops\$,\$ we get\$\oint {B.dL = } {\mu _0}{I_{enclosed}}\$For the smaller loop\$,\$\$ \Rightarrow B \times 2\pi \dfrac{a}{2} = {\mu _0} \times \dfrac{1}{{\pi {a^2}}} \times {\left( {\dfrac{a}{2}} \right)^2}\$\$ = {\mu _0}I \times \dfrac{1}{4} = \dfrac{{{\mu _0}I}}{4}\$\$ \Rightarrow {B_1} = \dfrac{{{\mu _0}I}}{{4\pi a}}\$\$B' \times 2\pi \left( {2a} \right) = {\mu _0}I\$\$\dfrac{B}{{B'}} = \dfrac{{{\mu _0}I}}{{4\pi a}} \times \dfrac{{4\pi a}}{{{\mu _0}I}} = 1\$Hence,option \$(C)\$ is correct answer.

Q: Define electric current. What is its \$SI\$ unit?

Electric current is basically the flow or charge of the electric charge in motion in a conductor. It is said to exist when there is a net flow of charge through the region.the current is given as the flow of charge per second:\$I=\dfrac{charge}{time}\$The SI unit of current is Ampere.

Q: Define \$1\$ ampere.

1 ampere is defined as 1 coloumb of charge per second. An ampere is a unit of measure of the rate of electron flow or current in an electrical conductor.

Q: A steady current flow in a metallic conductor of non-uniform cross-section. The quantity/quantities remaining constant along the whole length of the conductor is/are:

When a steady current flows in a metallic conductor of non-uniform cross-section then the drift speed is \$V_d=I/neA\$ and the electric field \$E=I/ \rho A\$\$\Rightarrow V_d\propto \dfrac{1}{A}\$ and \$E\propto \dfrac{1}{A}\$\$\Rightarrow\$ Only current remains constant.In a metallic conductor of non-uniform cross-section, only the current remains constant along the entire length of the conductor.

Q: S.I. unit of electric current is:

\$\text{Electric current is defined as the rate of flow of charge}\$\$\text{Since the charge is measured in coulombs and time in seconds, the electric current unit is Coulomb/Sec ( C/s )}\$\$\text{Where, coulomb/sec is defined as Ampere}\$ \$\text{So the Ampere is the SI unit of the current.}\$Hence Option A

Q: A current passes through a wire of non-uniform crosssection. Which of the following quantities are independent of the cross-section?

By conservation of charge and continuity equation, the current is same throughout a wire. Because current is defined as the charge crossing in a given time interval, option A is correct.By definition, \$I = nq {v}^{}_{d}\$ , where, \${v}^{}_{d} \$, is the drift velocity. It varies with cross section. So, B is incorrect. Due to non uniformity of cross section, the current density, defined asCurrent density \$= \dfrac{Current}{Area} \$ varies. So C is incorrect.The charge carrier density or free electron density is a property of material and temperature only. It does not depend upon cross section. So, D is correct.

Q: The rate flow of electric charge is called ................ .

An electric current is a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire. It can also be carried by ions in an electrolyte.

Q: A steady current is passing through a linear conductor of non uniform cross-section. The net quantity of charge crossing any cross section per second is

The quantity of charge passing through any cross-section per second is nothing but current flowing in the conductor.As given, the current is steady current, means current is uniform throughout the cross-section. Hence it is independent of Area of cross section.

Q: Is electric current a scalar or vector quantity? State the standard unit of electric current.

Current is a vector because it have a magnitude and a direction. But the thing is a vector always obey the law of addition of vectors.sincecurrent doesn't obey it and it follows algebraic addition,currents a scalar. Also, current is written as the dot product of current density vector and the area vector. Cgs unit is biot.