Electric Current, Ohm's Law and Drift of Electrons Class 12 Notes | EduRev

Physics Class 12

JEE : Electric Current, Ohm's Law and Drift of Electrons Class 12 Notes | EduRev

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What is Electric Current?

Electric Current is the rate of flow of electrons in a conductor. The SI Unit of electric current is the Ampere.

  • Our ancestors relied on fire for light, warmth and cooking. Today at the flick of a switch, turn of a knob or the push of a button we have instant power. This is possible because of the electric current.
  • From the basic bread toaster, baking oven to the commonly used television all require an electric current to operate. The most common device, mobile phones use the electric current to charge the battery for the operation. Besides playing a major part at home, electricity also plays an important role in industries, transportation and communication

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

  • Electrons are minute particles that exist within the molecular structure of a substance. Sometimes, these electrons are tightly held, and other times they are loosely held. When electrons are loosely held by the nucleus, they are able to travel freely within the limits of the body. 
  • Electrons are negatively charged particles hence when they move a number of charges moves and we call this movement of electrons as electric current. It should be noted that the number of electrons that are able to move governs the ability of a particular substance to conduct electricity. 
  • Some materials allow current to move better than others.

Based on the ability of the material to conduct electricity, materials are classified into Conductors, Insulators & Semiconductor.

1. Conductor

  • In some materials, the outer electrons of each atom or molecules are only weakly bound to it. These electrons are almost free to move throughout the body of the material and are called free electrons. 
  • They are also known as conduction electrons. When such a material is placed in an electric field, the free electrons move in a direction opposite to the field. Such materials are called conductors.
  • Examples of conductors: Human body, aqueous solutions of salts and metals like iron, silver and gold.
    Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Did you know?

Silver is the best conductor of electricity.

2. Insulator 

  • Another class of materials is called insulators in which all the electrons are tightly bound to their respective atoms or molecules. 
  • Effectively, there are no free electrons. When such a material is placed in an electric field, the electrons may slightly shift opposite to the field but they can't leave their parent atoms or molecules and hence can't move through long distances. 
  • Such materials are also called dielectrics.
    Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

3. Semiconductor

  • In semiconductors, the behaviour is like an insulator at low levels of temperature. But at higher temperatures, a small number of electrons are able to free themselves and they respond to the applied electric field. 
  • As the number of free electrons in a semiconductor is much smaller than that in a conductor, its behaviour is in between a conductor and an insulator and hence, the name semiconductor. 
  • A freed electron in a semiconductor leaves a vacancy in its normal bound position. These vacancies also help in conduction. Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev
    Semiconductors

Try yourself:Which of the following is the most conductive element?
View Solution

Unit of Electric Current

  • The magnitude of electric current is measured in coulombs per second. 
  • The SI unit of electric current is Ampere and is denoted by the letter A. 
  • Ampere is defined as one coulomb of charge moving past a point in one second. If there are 6.241 x 1018 electrons flowing through our frame in one second then the electrical current flowing through it is ‘One Ampere.’
  • The unit Ampere is widely used within electrical and electronic technology along with the multipliers like milliamp (0.001A), microamp (0.000001A), and so forth.

Properties of Electric Current

Electric current is an important quantity in electronic circuits. We have adapted electricity in our lives so much that it becomes impossible to imagine life without it. Therefore, it is important to know what is current and the properties of the electric current.

  • We know that electric current is the result of the flow of electrons. The work done in moving the electron stream is known as electrical energy. Electrical energy can be converted into other forms of energy such as heat energy, light energy, etc. For example, in an iron box, electric energy is converted to heat energy. Likewise, the electric energy in a bulb is converted into light energy.
  • There are two types of electric current known as alternating current (AC) and direct current (DC). 
  • The direct current can flow only in one direction, whereas the alternating direction flows in two directions. 
  • Direct current is seldom used as a primary energy source in industries. It is mostly used in low voltage applications such as charging batteries, aircraft applications, etc. Alternating current is used to operate appliances for both household and industrial and commercial use.
  • The electric current is measured in ampere. One ampere of current represents one coulomb of electric charge moving past a specific point in one second.

1 ampere = 1 coulomb / 1 second

  • The conventional direction of an electric current is the direction in which a positive charge would move. Henceforth, the current flowing in the external circuit is directed away from the positive terminal and toward the negative terminal of the battery.

What is Ohm's Law?

Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature remain constant.

  • Ohm’s Law of Current Electricity is named after the scientist ”Ohm”. Most basic components of current electricity are voltage, current, and resistance. Ohm’s law shows a simple relation between these three quantities.

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

  • Voltage = Current × Resistance
    V = I×R
    where V= voltage, I= current and  R= resistance. The SI unit of resistance is ohms and is denoted by Ω
  • In order to establish the current-voltage relationship, the ratio V / I remains constant for a given resistance, therefore a graph between the potential difference(V) and the current (I) must be a straight line.
  • This law helps us in determining either voltage, current or impedance or resistance of a linear electric circuit when the other two quantities are known to us. It also makes power calculation simpler.

Ohm’s Law Equation: V = IR, where V is the voltage across the conductor, I is the current flowing through the conductor and R is the resistance provided by the conductor to the flow of current.

Ohm’s Law Magic Triangle

You can make use of the Ohm’s law magic triangle to remember the different equations for Ohm’s law used to solve for different variables(V, I, R).    

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

If the value of voltage is asked and the values of the current and resistance are given, then to calculate voltage simply cover V at the top. So, we are left with the I and R or I X R. So, the equation for Voltage is Current multiplied by Resistance. Examples of how the magic triangle is employed to determine the voltage using Ohm’s law is given below.


Example 1: If the resistance of an electric iron is 50 Ω and a current of 3.2 A flows through the resistance. Find the voltage between two points.

If we are asked to calculate the value of voltage with the value of current and resistance given to us, then cover V in the triangle. Now, we are left with I and R or more precisely I × R.

Therefore, we use the following formula to calculate the value of V:

V = I × R

Substituting the values in the equation, we get

V = 3.2 A × 50 ÷ = 160 V


Example 2: An EMF source of 8.0 V is connected to a purely resistive electrical appliance (a light bulb). An electric current of 2.0 A flows through it. Consider the conducting wires to be resistance-free. Calculate the resistance offered by the electrical appliance.

When we are asked to find out the value of resistance when the values of voltage and current are given, then we cover R in the triangle. This leaves us with only V and I, more precisely V ÷ I.

Substituting the values in the equation, we get

R = V ÷ I

R = 8 V ÷ 2 A = 4 Ω

Applications of Ohm’s Law 

The main applications of Ohm’s law are:

  • To determine the voltage, resistance or current of an electric circuit.
  • Ohm’s law is used to maintain the desired voltage drop across the electronic components.
  • Ohm’s law is also used in DC ammeter and other DC shunts to divert the current.

Limitations of Ohm’s Law

Following are the limitations of Ohm’s law:

  • Ohm’s law is not applicable for unilateral electrical elements like diodes and transistors as they allow the current to flow through in one direction only.
  • For non-linear electrical elements with parameters like capacitance, resistance etc the voltage and current won’t be constant with respect to time making it difficult to use Ohm’s law.

Electric Current and Current Density

  • Electric charges in motion constitute an electric current. Any medium having practically free electric charges, free to migrate is a conductor of electricity. The electric charge flows from a higher potential energy state to a lower potential energy state.
    Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev
  • Positive charge flows from higher to lower potential and negative charge flows from lower to higher. Metals such as gold, silver, copper, aluminium etc. are good conductors. 
  • When charge flows in a conductor from one place to the other, then the rate of flow of charge is called electric current (I). 
  • When there is a transfer of charge from one point to other point in a conductor, we say that there is an electric current through the area. If the moving charges are positive, the current is in the direction of motion of charge. 
  • If they are negative the current is opposite to the direction of motion. If a charge ΔQ crosses an area in time Δt then the average electric current through the area, during this time as
    (i) Average current Iav = ΔQ/Δt
    (ii) Instantaneous current  
    Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Example 3:  If q = 2t2, find current at t = 2 sec ?

i = dq/dt, i = 4t

∴ i at 2 sec = 4 × 2 = 8 A

  • Current is a macroscopic quantity and deals with the overall rate of flow of charge through a section. To specify the current with direction in the microscopic level at a point, the term current density is introduced. Current density at any point inside a conductor is defined as a vector having magnitude equal to current per unit area surrounding that point. Remember area is normal to the direction of charge flow (or current passes) through that point.
  • Current density at point P is given by
    Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRevElectric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev
  • If the cross-sectional area is not normal to the current but makes an angle θ with the direction of current
    Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev
  • Current density Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRevis a vector quantity. Its direction is same as that of Its S.I. unit is ampere/m2 and dimension [L–2A].

Example 4: An electron beam has an aperture 1.0 mm2. A total of 6.0 × 1010 electrons go through any perpendicular cross-section per second. Find (a) the current and (b) the current density in the beam.

The total charge crossing a perpendicular cross-section in one second is

q = ne

= 6.0 × 1016 × 1.6 × 10-19 C

= 9.6 × 10-3 C

The current is

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

As the charge is negative, the current is opposite to be direction of motion of the beam.

(b) The current density is

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev


Try yourself:Give the SI unit of current density and its dimensional formula.
View Solution


Drift of Electrons & the Origin of Resistivity

  • The net velocity of the circuit is zero when electrons move randomly in the circuit and the electric field is not applied to the circuit. 
  • Drift force is the force driving the electrons through a conductor and the force opposing the drift force is resistivity.

What is Resistance or Resistivity?

The tendency of a material/device towards resistance is the resistivity of the device/circuit. The SI unit of resistivity is ohm-meter. The unit length across the cross-sectional area of the device is also resistivity. Therefore, the nature and temperature of the material also define resistivity (σ).

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

The graph of resistivity as follows. The graphs depict current (I) to voltage (V) ratio, whereas, dotted line A, B, C shows the idealized graph. After a certain amount of current, the device starts resisting to the current flowing in the system and the resistivity becomes constant.


Drift of Electrons

  • The free electrons in a conductor have random velocities and move in random directions. When current is applied across the conductor the randomly moving electrons are subjected to electrical forces along the direction of the electric field.
  • Due to this electric field, free electrons still have their random moving nature, but they will move through the conductor with a certain along with force. The net velocity in a conductor due to the moving of electrons is referred to as the drift of electrons.


Drift Velocity

Drift velocity is defined as the velocity with which the free electrons get drifted towards the positive terminal under the effect of the applied external electric field. 

In addition to its thermal velocity, due to acceleration given by the applied electric field, the electron acquires a velocity component in a direction opposite to the direction of the electric field. The gain in velocity due to the applied field is very small and is lost in the next collision.

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

At any given time, an electron has a velocity,
Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev the thermal velocity and Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRevthe velocity acquired by the electron under the influence of the applied electric field.
τ= the time that has elapsed since the last collision. Similarly, the velocities of the other electrons are

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev
The average velocity of all the free electrons in the conductor is equal to the drift velocity Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev of the free electrons
Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev
Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev
Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Note: Order of drift velocity is 10–4 m/s.


➢ Relation between current and drift velocity

Let n = number density of free electrons and A = area of cross–section of conductor.
Number of free electrons in conductor of length L = nAL, Total charge on these free electrons Δq = neAvd
Time taken by drifting electrons to cross conductor
Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Mobility

  • Conductivity arises from mobile charge carriers. In metals, these mobile charge carriers are electrons; in an ionised gas, they are electrons and positive charged ions; in an electrolyte, these can be both positive and negative ions.
  • An important quantity is the mobility µ defined as the magnitude of the drift velocity per unit electric field:
    Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev


Example 5: Calculate the drift speed of the electrons when 1 A of current exists in a copper wire of cross-section 2 mm2. The number of free electrons in 1 cm3 of copper is 8.5 × 1022.

We have

j = nevd

or,

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

We see that the drift speed is indeed small.


Example 6: Calculate the resistance of an aluminium wire of length 50 cm and cross-sectional area 2.0 mm2. The resistivity of aluminium is ρ = 2.6 × 10-8m ?

The resistance is 

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

We arrived at Ohm's law by making several assumptions about the existence and behaviour of the free electrons. These assumption are not valid for semiconductors, insulators, solutions etc. Ohm's law cannot be applied in such cases.


Example 7: The dimensions of a conductor of specific resistance r are shown below. Find the resistance of the conductor across AB, CD and EF.

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev


Example 8: A portion of length L is cut out of a conical solid wire. The two ends of this portion have circular cross-sections of radii r1 and r2 (r2 > r1). It is connected lengthwise to a circuit and a current i is flowing in it. The resistivity of the material of the wire is ρ. Calculate the resistance of the considered portion and the voltage developed across it.

If follows from the figure, that

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

 Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Therefore,

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev               

Therefore, 

 Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

      

Example 9: The space between two coaxial cylinders, whose radii are a and b (where a < b as in (figure shown) is filled with a conducting medium. The specific conductivity of the medium is σ.

 Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

(a) Compute the resistance along the length of the cylinder.

(b) Compute the resistance between the cylinders in the radial direction. Assume that the cylinders are very long as compared to their radii, i.e., L >> b, where L is the length of the cylinders.

(a) Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

(b) From Ohm's law, we have

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Assuming radial current density. Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev becomes

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

and, therefore, 

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Here we have used the assumption that L >> b so that Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev and are in cylindrically symmetric form. The potential drop across the medium is thus :

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev 

The resistance

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev


Method 2: We split the medium into differential cylindrical shell elements of width dr, in series. The current flow is cylindrically symmetric (L >> b). The area through which the current flows across a shell of radius r is A(r) = 2πrL. The length the current flows, passing through a shell of radius r is dr. Therefore, the resistance of the shell of radius r is :

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

Since the shells are connected in a series, we have

Electric Current, Ohm`s Law and Drift of Electrons Class 12 Notes | EduRev

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