The NCERT Solutions for Class 12 Physics Chapter 3 covers topics under "Current Electricity", including some of the basic laws related to steady electric currents, such as Ohm’s Law, Kirchoff’s Law, EMF and more. Some important questions and problems related to current electricity for class 12 are also covered in the chapter. Students are encouraged to go through the NCERT Solutions for a thorough understanding of the chapter. All the important questions for Class 12 Current Electricity chapter are prepared by subject matter experts and provide step-wise solutions for each, ensuring that students are well prepared for the exam.
Topics Covered in Chapter 3:
1. Introduction
2. Electric Current
3. Electric Currents In Conductors
4. Ohm’s Law
5. Drift of Electrons and the Origin of Resistivity
6. Mobility
7. Limitations of Ohm’s Law
8. Resistivity of Various Materials
9. Temperature Dependence of Resistivity
10. Electrical Energy, Power
11. Combination of Resistors – Series and Parallel
12. Cells, Emf, Internal Resistance
13. Cells in Series and in Parallel
14. Kirchhoff’s Rules
15. Wheatstone Bridge
16. Meter Bridge
17. Potentiometer

Many centuries ago, human beings used fire for light, warmth, and to cook. But now, thanks to the technological advancements in society, humans have electric power at the flick of a switch or push of a button. This is made possible because of electricity or electric current, which has revolutionized modern life. From using electric stoves for cooking to using geysers for a hot bath, almost every aspect of human life relies on electricity to function. Apart from home usage, electricity is required in industries, transportation, communication and more.

Physics Class 12 Chapter 3 covers all the topics related to electric current, including what is electric current, unit of current, formulas, laws, applications, and more.

Electric current is defined as the rate of flow of electrons or their charge through a conductor. Ampere is the SI Unit of electric current as is represented by “A”.

When the connection between a nucleus and its electrons is weak, the electrons are free to move. This movement of electrons that are negatively charged particles is known as electric current. The medium through which the electrons travel determines how fast the current can flow. Some materials allow more electrons to flow than others. These materials are called conductors, while materials that restrict the flow of electrons are called insulators.

Materials that let electrons flow freely from one particle to another are called conductors. They enable charge to be transferred through the electrons. An electric current is produced through the flow of electrons within the conductor. The force that causes the current to flow through the conductor is called voltage.

Examples of conductors include the human body; metals such as iron, aluminium, gold, copper, silver, etc.; salt water, and more.

Conditions required for the flow of electrons in a conductor are as follows:

- The circuit must have an energy source, such as a battery, to generate voltage or the force required to drive the flow of current in a conductor. In the absence of voltage, electrons move freely without direction, causing no current flow. The pressure created by the voltage on the electrons causes the current to flow in a particular direction.
- The circuit must contain conducting materials and should be a closed loop through which electrons can flow. When the circuit switch is turned ON, the circuit is complete.

Ohm’s Law states that the potential difference or voltage across a conductor is directly proportional to the electric current flowing through it, given that the conductor’s temperature and other physical conditions remain constant.

Mathematically, the Ohm's Law formula is written as:

V = IR, where V is the voltage, I is the current, and R is the resistance of the conductor, which is constant of proportionality.

The Ohm’s law equation can be rearranged to find the current: I = V/R,

or to find the resistance: R = V/I.

**Solved example of Ohm’s Law:**

The battery of a remote control has an EMF of 10V. If the battery has internal resistance of 0.5Ω, what is the current that the battery can generate?

**Answer:**

Given R = 0.5Ω and V = 10V, we have to find I.

Using Ohm’s law: V = IR, we can rearrange the equation to find I:

I = V/R

I = 10/0.5 = 20.

Therefore, the current drawn from the battery is 20A.

When there is no electric field applied to a circuit, its net velocity is zero, as the electrons move randomly in the circuit. In the case where an electric field is applied, the average velocity at which the electrons move towards the positive end of the conductor is called the drift velocity of electrons and is given by:

, where 𝛕 = relaxation time, E = field, m = mass, and e = electron. The drift velocity of electrons is of the order 10-4ms-1.

The electric current in relation to drift velocity is given by:

, where n = number density of free electrons, e = electronic charge, a = cross-sectional area of conductor, and Vd = drift velocity of an electron.

Resistivity is the force opposing the drift force and its SI unit is ohm-meter. The unit length of the conductor’s cross-section also determines resistivity. Therefore, the characteristics and temperature of the conductor also impact resistivity (σ). After a certain amount of current is applied, the conductor’s resistance against the current flowing in the circuit increases, making the resistivity constant. Resistivity is given by:

σ = RA/L.

The magnitude of the drift velocity per unit electric field is called the mobility, represented by µ. It is the measurement of the speed of an electron through a semiconductor or a metal where an electric field is applied. The formula for mobility is and the SI unit is m/Vs.

Here are some limitations of Ohm’s law with examples:

- Ohm’s law is not applicable to unilateral networks as the current flows only in one direction in such networks. Changing the direction of the voltage V but keeping the magnitude the same does not generate a current I of the same magnitude in the opposite direction. Examples of these types of circuits are diodes and transistors.
- Ohm’s law is not applicable to non-linear circuits because the resistance value in such circuits is not constant and changes depending on the current or voltage changes. A thyristor is an example of a non-linear circuit.
- In some cases, when the current increases, the temperature also increases, in a light bulb, for example, in which the temperature of the filament rises as the current increases. Therefore, Ohm’s law does not apply here.
- Ohm’s law is also not applicable on some semiconductors, such as silicon and germanium. These are known as non-Ohmic conductors.

A highly resistant material resists the flow of electrons, while a low-resistant material allows the electrons to flow smoothly through the material.

Good conductors such as metals, like gold and copper, have low resistivity, while insulators such as glass are highly resistant. Semiconductors such as silicon are partially resistant.

In perfect conductors, the resistivity is zero and in perfect insulators, it is infinite.

Here are some materials with their resistivity in Ωm at 0°C:

**Conductors**:- Silver: 1.6 × 10–8
- Copper: 1.7 × 10–8
- Aluminium: 2.7 × 10–8
- Tungsten: 5.6 × 10–8
- Iron: 10 × 10–8
- Platinum: 11 × 10–8
- Mercury: 98 × 10–8
- Nichrome: ~100 × 10–8
- (alloy of Ni, Fe, Cr) Manganin (alloy): 48 × 10–8
**Semiconductors**- Carbon (graphite): 3.5 × 10–5
- Germanium: 0.46
- Silicon: 2300
**Insulators**- Pure Water: 2.5 × 105
- Glass: 1010 – 1014
- Hard Rubber: 1013 – 1016
- NaCl: ~1014
- Fused Quartz: ~1016

In some materials, temperature affects the resistivity. Different materials have different levels of dependence on temperatures of resistivity. The formula for the temperature dependence of resistivity of metals over a limited range of temperatures is given by:

, where ρT is the resistivity at a temperature T, ρ0 is the same at a reference temperature T0 , and α is the temperature coefficient of resistivity.

Some materials such as nichrome, which is an alloy of nickel, iron, and chromium, have a low temperature dependence of resistivity. Manganin and constantan behave similarly. Since the resistance values of these materials change very little with temperatures, they are commonly used in wire-bound standard resistors.

The resistance values of semiconductors decrease as the temperature increases because with the increase in temperature, the average speed of the electrons also increases. This causes more frequent collisions, thereby reducing resistance. The temperature dependence of resistivity formula for such materials is given by:

Therefore, ρ is inversely proportional to both the number of free electrons n per unit volume and the average time 𝛕 between collisions.

For insulators, n increases with temperature, compensating any decrease in 𝛕 in the resistivity formula for semiconductors, such that ρ decreases with temperature.

When electrons move from one end of a material to another, the kinetic energy or the potential energy generated is called electrical energy. Current or electricity is thus constituted by the movement of charged particles along the medium.

Consider a conductor carrying the current I, and potential difference V between two points A and B. The electric potential of A and B is V(A) and V(B) respectively. If current flows from A to B, then V(A) >V(B), and the potential difference across the points AB is V = V(A) – V(B) > 0.

Since electric current is the rate of flow of charge through the cross-section of a conductor, the current is given by I = ∆Q/∆t, where ∆Q is the amount of electric charge moving across the conductor over a time period ∆t.

The potential energy of charge Q at A is Q V(A) and at B is Q V(B). The change in the potential energy is given by:

∆Upot = final potential energy – initial potential energy

= ∆Q [(V(B) – V(A)] = –∆Q V

= –I V∆t (since I = ∆Q/ ∆t)

If the electrons in the conductor move without collisions, their kinetic energy also changes. Therefore, by the law of conservation of energy:

∆K = –∆Upot = I V Δt > 0

The quantity of energy lost as heat in a conductor over a time period Δt is:

ΔW = V ΔQ = VI Δt

Electrical power is the rate at which the work is done or the energy is used in moving the electrons from one end of the material to the other. It is denoted by P.

The SI unit of power is watt (W), and the formula of power is given by:

P = VI

Applying Ohm's law:

P = I² R = V²/R

This equation can be used to find the amount of power lost as the current I travels through a conductor with resistance R.

Resistors are added in circuits to control the flow of current and reduce the voltage within the circuit. Some circuits may have multiple resistors arranged in different combinations to moderate the flow of electrons. Resistors may be arranged in two types of combinations: series and parallel.

A series combination of two resistors is when only one of the resistor end points is joined. If more resistors are added with the series combination of the two, then all of them are in series. In a series circuit, the same amount of current flows through all the resistors but the voltage is different across each resistor. Even if one resistor is broken, no current will flow in the entire series circuit. The formula for the total resistance in a series circuit is given by:

Rtotal = R1 + R2 + ….. + Rn

For example, in a series circuit, if there are three resistors with values 50Ω, 100Ω, and 75Ω, respectively, then the total resistance of the series circuit is (50 + 100 + 75)Ω = 225Ω.

When two or more resistors are connected in parallel combination, the voltage is the same across the resistors but the current is different. Here, the current in the circuit remains unaffected even if one resistor is disconnected. The formula for the total resistance in a parallel circuit is given by:

1/Rtotal = 1/R1 + 1/R2 + ….. + 1/Rn

If the resistors with values 50Ω, 100Ω, and 75Ω are connected in parallel combination, then the total resistance of the circuit is:

1/Rtotal = 1/50 + 1/100 + 1/75 = (6 + 3 + 4)/300 = 13/300

Rtotal = 300/13 = 23.07Ω.

A cell is a device that stores chemical energy and converts it into electrical energy through chemical reactions or vice versa. Two or more cells make up an electrical battery, which stores energy and provides the electromotive force or EMF required for the circuit to function.

Each cell consists of two half-cells that are connected in series by a conductive electrolyte. The electrolyte is made up of negatively and positively charged ions, known as anions and cations, respectively. One half-cell is made up of the electrolyte and the negative electrode or the anode, which attracts the anions, while the other half-cell is made up of the electrolyte and the positive electrode or the cathode, which attracts the cations.

The redox reactions (i.e. reduction and oxidation) happen at the same time, powering the battery. During charging, the cathode gains electrons, while the anode loses electrons. The reverse happens while discharging.

When there is no current flowing through the cell, the electrolyte has the same potential (EMF) throughout the cell. The potential of the cell is equal to the difference of the potential of the electrodes. The anode has a positive potential V+ and the cathode has a negative potential –V–. The potential difference between V+ and V– is the Electromotive Force (EMF) of the cell which is given by:

ξ = V+ − (−V−) = V+ + V−

Cells arranged in series are joined end-to-end such that each cell has the same amount of current flowing through it. In a series connection, the EMF of the battery (E) is the sum of the EMF of the individual cells.

E = E1 + E2 + E3 + …En

Similarly, the internal resistance of the battery (r) is the sum of the internal resistances of each cell.

r = r1 + r2 + r3 + … + rn

Cells arranged in parallel are joined such that the positive terminals are connected to each other and the negative terminals are connected to each other. In a parallel circuit, the current is divided among each cell. If the EMF of each cell is identical, then the EMF of the battery is equal to the EMF of each cell in the parallel circuit. The internal resistance of the parallel circuit is:

r = (1/𝑟1 + 1/𝑟2 + 1/𝑟3 + ... 1/𝑟𝑛 )-1

German physicist Gustav Robert Kirchhoff formulated two laws that can be applied in electrical circuits:

- Kirchhoff’s Current Law or Kirchhoff’s First Law or Junction Rule: The first law states that in an electrical circuit, at any node or junction, the total amount of current entering the node is the same as the total amount of current leaving the node. In other words, adding the total current flowing in and subtracting the total current flowing out of the node is equal to null, i.e. Iexit + Ienter = 0.
- Kirchhoff’s Voltage Law or Kirchoff’s Second Law or Loop Rule: The second law states that the algebraic sum of changes in potential around any closed loop is zero.

Wheatstone Bridge Circuit, also known as the resistance bridge circuit, contains two known resistors, one unknown resistor, and one variable resistor. They are connected in the form of a bridge. The Wheatstone Bridge is used to measure the unknown resistance. It does this by balancing the bridge circuit’s two legs. A galvanometer and an electromotive force source are also present in the wheatstone bridge circuit. The EMF source is attached between points a and b and the galvanometer is attached between points c and d. The current flowing through the galvanometer is dependent on its potential difference.

The Wheatstone Bridge principle is that of null deflection. This means that the ratio of one pair of resistances is equal to that of the second pair and the amount of current flowing through the circuit is zero. Under normal circumstances, the bridge remains unbalanced, with the current flowing through the galvanometer. The bridge is in balance when there is zero current flowing through the galvanometer and can be balanced by modifying the known and variable resistances.

A meter bridge is used to calculate the unknown resistance of a metal coil by applying the Wheatstone bridge principle. It is called meter bridge as it consists of a constantan or manganin wire, 1m in length, with uniform cross-sectional area.

A potentiometer is used to control the EMF and internal resistance of a cell by providing a variable resistance. This gives a variable potential difference between two points in a circuit. A potentiometer is essentially a three-terminal resistor with an adjustable arm that regulates the resistance in the circuit.

The following are some applications of a potentiometer:

- Potentiometers are used to control the volume in various audio equipment.
- Potentiometers are used to control the picture brightness and contrast in televisions.

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MSVgo NCERT Solutions for Class 12 Physics Chapter 3 is reliable because the solutions have been prepared in a detailed manner by subject matter experts. Using MSVgo NCERT Solutions will be helpful for students preparing for exams as there are numerous exam-style questions and exercises to ensure rigorous practice. Watching MSVgo videos on the chapter will enhance learning and boost confidence in the topic.

**2 . Is the NCERT Solutions for Class 12 Physics Chapter 3 the best reference guide for the students?**

Yes, the NCERT Solutions for Class 12 Physics Chapter 3 is the best reference guide for students as it covers all the topics related to Current Electricity, including the definitions, theorems, derivations, explanations, and step-by-step problems. This is a useful tool while studying as it follows the CBSE board requirements, allowing students to prepare in alignment with the board exams.

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