Ncert Books Class 12 Physics Chapter 3 Free Download

The numericals from this chapter often carry significant weightage. Students should focus on problems based on:

• Kirchhoff's Laws: Solving complex circuits to find current in different branches and potential differences between points.
• Potentiometer and Metre Bridge: Calculating unknown resistance, comparing EMFs, and finding the internal resistance of a cell based on balancing lengths.
• Combination of Resistors and Cells: Finding the equivalent resistance or EMF in complex series, parallel, or mixed groupings.
• Drift Velocity and Resistivity: Problems connecting microscopic properties (like drift velocity, relaxation time) with macroscopic properties (current, resistance).

For 3-mark questions, the focus is often on concise derivations of fundamental relationships. Important derivations include:

• Deriving the expression for drift velocity, v_d = (eE/m)τ.
• Establishing the relationship between electric current and drift velocity: I = nAev_d.
• Deducing Ohm's law (V=IR) from the first principles using the relationship between current and drift velocity.
• Deriving the expression for the resistivity of a material in terms of electron density and relaxation time: ρ = m/(ne²τ).

The vector form of Ohm's law relates current density (J), conductivity (σ), and the electric field (E) at any point inside a conductor. It is stated as J = σE.

Derivation: We know that I = nAev_d, and drift velocity v_d = (eE/m)τ. Substituting v_d, we get I = nAe(eE/m)τ = (ne²Aτ/m)E. Current density J = I/A = (ne²τ/m)E. Since conductivity σ = (ne²τ/m), we arrive at J = σE.

This form is more fundamental because V=IR applies to a specific conductor (a macroscopic object), whereas J=σE describes the electrical property of the material itself (a microscopic property) at a point, independent of the conductor's dimensions.

This is a crucial conceptual point.

• Junction Rule (Conservation of Charge): This rule states that the algebraic sum of currents entering a junction is equal to the sum of currents leaving it. This implies that charge does not accumulate or get lost at any point in a steady circuit. The rate at which charge arrives at a junction must equal the rate at which it leaves, which is a direct consequence of the law of conservation of charge.
• Loop Rule (Conservation of Energy): This rule states that the algebraic sum of changes in potential around any closed loop is zero. A change in potential (ΔV) is related to the work done per unit charge (W/q). As a charge moves around a closed loop and returns to its starting point, its net change in energy must be zero. Therefore, the total energy supplied by the sources (like batteries) must be equal to the energy dissipated in the components (like resistors), which is an expression of the law of conservation of energy.

The key difference lies in the cell's state of operation:

• EMF (Electromotive Force): This is the maximum potential difference between the two terminals of a cell when it is in an open circuit (i.e., no current is being drawn). It represents the total energy supplied per unit charge by the cell.
• Terminal Voltage (V): This is the potential difference between the terminals of a cell when it is in a closed circuit (i.e., current is flowing). It is always less than the EMF during discharging due to the potential drop across the cell's internal resistance (r), given by V = E - Ir.

The terminal voltage can exceed the EMF only during the charging of the cell. In this case, an external source drives current into the positive terminal of the cell. The equation becomes V = E + Ir, making V greater than E.

The preparation strategy differs because the exam patterns test different skills:

• CBSE Board Exams: The focus is on systematic problem-solving and theoretical understanding. Important questions include long-answer derivations (e.g., potentiometer, Wheatstone bridge), defining key terms, explaining principles, and solving numericals with clear, step-by-step working.
• NEET/JEE Exams: The focus is on speed, accuracy, and conceptual application in a multiple-choice format. Questions are often trickier, involving complex circuit configurations, conceptual traps (e.g., non-ideal instruments), and quick application of formulae. Derivations are not asked directly, but their results are crucial for fast problem-solving.

The temperature dependence of resistivity is a key differentiator for materials:

• Conductors: For conductors like copper, resistivity increases with temperature. This is because as temperature rises, the thermal agitation of metal ions increases, leading to more frequent collisions with electrons and a decrease in the average relaxation time (τ).
• Semiconductors: For semiconductors like silicon, resistivity decreases exponentially with temperature. Although collisions increase, the rise in temperature provides enough energy to break covalent bonds, significantly increasing the number density of charge carriers (electrons and holes), which dominates over the effect of increased collisions.
• Insulators: The resistivity is extremely high. It also decreases with temperature, but a much higher temperature is needed to create a noticeable increase in charge carriers compared to semiconductors.