Current Electricity Class 12 Chapter Notes

Key Terms and Definitions

Electric Current (I)

The rate of flow of electric charge through any cross-section of a conductor. S.I. unit is Ampere (A). I = dQ/dt.

Drift Velocity (v_d)

The average velocity with which free electrons in a conductor get drifted towards the positive end of the conductor under the influence of an external electric field.

Mobility (μ)

The magnitude of the drift velocity per unit electric field. μ = v_d / E. S.I. unit is m²V⁻¹s⁻¹.

Ohm's Law

At constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends. V ∝ I or V = IR.

Resistance (R)

The opposition offered by a conductor to the flow of electric current. R = ρl/A. S.I. unit is Ohm (Ω).

Resistivity (ρ)

The resistance of a conductor of unit length and unit cross-sectional area. It is an intrinsic property of the material.

Electromotive Force (EMF)

The maximum potential difference between the two terminals of a cell when no current is drawn from it (i.e., in an open circuit).

Kirchhoff's First Law (Junction Rule)

The algebraic sum of currents entering a junction is equal to the algebraic sum of currents leaving it. Based on the conservation of charge.

Kirchhoff's Second Law (Loop Rule)

The algebraic sum of changes in potential around any closed loop involving resistors and cells is zero. Based on the conservation of energy.

Understanding Drift Velocity and its Relation to Current

In a metallic conductor, free electrons are in continuous random motion, colliding with each other and with the positive ions of the lattice. Their average thermal velocity is zero, so there is no net flow of charge. When an electric field (E) is applied across the conductor (by connecting it to a battery), each electron experiences an electrostatic force F = -eE. This force accelerates the electron in a direction opposite to the field. However, this acceleration is short-lived as the electron soon collides with a lattice ion, losing its gained kinetic energy. It then accelerates again, collides again, and this process repeats. The result is that the electrons acquire a small, constant average velocity, superimposed on their random motion, directed opposite to the electric field. This average velocity is called the drift velocity (v_d).

Although v_d is very small (of the order of 10⁻⁴ m/s), the electric field that causes this drift travels at nearly the speed of light. This is why a bulb lights up almost instantly when you flip a switch. The relationship between current (I) and drift velocity is fundamental: I = nAev_d, where n is the number density of free electrons, A is the cross-sectional area, and e is the charge of an electron. This equation beautifully connects the macroscopic quantity (current) with the microscopic behavior of charge carriers.

Formula Sheet & Must-Remember Concepts

• Ohm's Law: V = IR. Vector form: J = σE, where J is current density and σ is conductivity.
• Resistance: R = ρl/A, where ρ is resistivity.
• Current & Drift Velocity: I = nAev_d.
• Relation between J, E, v_d: J = neV_d and v_d = (eE/m)τ, where τ is the relaxation time.
• Temperature Dependence of Resistance: R_T = R₀[1 + α(T - T₀)]. For conductors, α is positive. For semiconductors, α is negative.
• Series Combination of Resistors: R_eq = R₁ + R₂ + ...
• Parallel Combination of Resistors: 1/R_eq = 1/R₁ + 1/R₂ + ...
• Internal Resistance (r): V = E - Ir (when cell is discharging), V = E + Ir (when charging).
• Power: P = VI = I²R = V²/R.
• Wheatstone Bridge (Balanced): P/Q = R/S. No current flows through the galvanometer.

Applying Kirchhoff's Laws to Solve Circuits

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Comparison: Resistors in Series vs. Parallel

Worked Mini-Examples

• {"heading":"Example 1: Equivalent Resistance","bodyMarkdown":"Question: Two resistors of 4Ω and 6Ω are connected in parallel. This combination is then connected in series with a 2.2Ω resistor. Find the total equivalent resistance.\nSolution:\n1. Parallel part: 1/R_p = 1/4 + 1/6 = (3+2)/12 = 5/12. So, R_p = 12/5 = 2.4Ω.\n2. Series part: The combination R_p is in series with 2.2Ω. R_eq = R_p + 2.2Ω = 2.4Ω + 2.2Ω = 4.6Ω."}
• {"heading":"Example 2: Drift Velocity","bodyMarkdown":"Question: A copper wire of area 2.0 mm² carries a current of 1 A. Given electron density n = 8.5 x 10²⁸ m⁻³. Calculate the drift velocity of electrons.\nSolution:\nUsing the formula I = nAev_d:\nv_d = I / (nAe)\nv_d = 1 / (8.5 x 10²⁸ x 2.0 x 10⁻⁶ x 1.6 x 10⁻¹⁹)\nv_d ≈ 1 / (27.2 x 10²) ≈ 0.0367 x 10⁻² m/s = 3.67 x 10⁻⁴ m/s."}

Board Exam Traps

A common mistake is in the sign convention for Kirchhoff's loop rule. Always decide your traversal direction first, then apply the rules consistently. If you move in the direction of the current, potential drops across a resistor (-IR). If you move from negative to positive terminal of a battery, potential gains (+E). Also, remember the difference between EMF (E) and terminal voltage (V). E is the property of the cell, while V is the potential difference across its terminals when current is flowing (V = E - Ir). Questions often test this subtle difference.

Practice Questions with Solutions

• Q: On what factors does the resistivity of a material depend? A: Resistivity depends on the nature of the material and its temperature. It does not depend on the dimensions (length, area) of the conductor.
• Q: Why are household appliances connected in parallel? A: To ensure each appliance gets the same voltage (e.g., 220V) and can be operated independently. If in series, they would have to share the voltage and switching one off would break the entire circuit.
• Q: What is the principle of a potentiometer? A: A potentiometer works on the principle that the potential drop across any portion of a wire of uniform cross-section and composition is directly proportional to its length, provided a constant current flows through it.
• Q: State the condition for a balanced Wheatstone bridge. A: The bridge is balanced when the ratio of resistances in the opposite arms are equal (P/Q = R/S), resulting in zero current through the galvanometer.

Frequently Asked Questions

Frequently Asked Questions