Current Electricity Class 12 Physics Chapter Notes

Key Terms and Definitions

Electric Current (I)

The rate of flow of electric charge through any cross-section of a conductor. Measured in Amperes (A). I = dQ/dt.

Current Density (J)

The electric current per unit area of cross-section of the conductor. It is a vector quantity. J = I/A. SI unit is A/m².

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. SI unit is m²V⁻¹s⁻¹.

Ohm's Law

States that the current flowing through a conductor is directly proportional to the potential difference across its ends, provided the physical conditions (temperature, pressure) remain unchanged. V ∝ I or V = IR.

Resistivity (ρ)

The electrical resistance of a conductor of unit cross-sectional area and unit length. It is an intrinsic property of the material. ρ = RA/L. SI unit is Ohm-meter (Ωm).

Electromotive Force (EMF)

The potential difference between the terminals of a cell when no current is drawn from it (in an open circuit). It is the work done by the source in driving a unit charge around the complete circuit.

Internal Resistance (r)

The resistance offered by the electrolyte and electrodes of a cell to the flow of current through it.

Must-Remember Formulas & Concepts

• Microscopic view of Current: I = n e A v_d, where n is the number density of free electrons, e is the charge of an electron, A is the cross-sectional area, and v_d is the drift velocity.
• Vector form of Ohm's Law: J = σE, where J is current density, σ is conductivity (1/ρ), and E is the electric field.
• Drift Velocity Formula: v_d = (eE/m)τ, where E is the electric field, m is the mass of the electron, and τ is the average relaxation time.
• Temperature Dependence of Resistance: R_T = R₀(1 + αΔT), where α is the temperature coefficient of resistance.
• Resistors in Series: R_eq = R₁ + R₂ + ... (Current is same, voltage divides)
• Resistors in Parallel: 1/R_eq = 1/R₁ + 1/R₂ + ... (Voltage is same, current divides)
• Relation between EMF (ε), Terminal Voltage (V), and Internal Resistance (r): V = ε - Ir (when the cell is discharging) and V = ε + Ir (when charging).
• Kirchhoff's First Law (Junction Rule): Based on conservation of charge. The algebraic sum of currents meeting at a junction is zero (ΣI = 0).
• Kirchhoff's Second Law (Loop Rule): Based on conservation of energy. The algebraic sum of changes in potential around any closed loop is zero (ΣΔV = 0).
• Wheatstone Bridge Balanced Condition: P/Q = R/S. No current flows through the galvanometer.
• Potentiometer Principle: When a constant current flows through a wire of uniform cross-section and composition, the potential drop across any length of the wire is directly proportional to that length (V ∝ L).

Understanding Drift Velocity and its Origin

The flow of current in a metallic conductor is due to the movement of free electrons. In the absence of an external electric field, these electrons are in continuous random motion, similar to the molecules of a gas. Their average thermal velocity is very high (around 10⁵ m/s), but their net velocity in any direction is zero, hence no net current. When an external electric field (E) is applied across the conductor, each electron experiences an electrostatic force F = -eE (opposite to the direction of E). This force accelerates the electron. However, this acceleration is short-lived as the electron frequently collides with the positive ions (kernels) of the metal lattice, losing its gained momentum. The average time interval between two successive collisions is called the relaxation time (τ). Between collisions, the electron accelerates, and then a collision occurs, randomizing its direction. The result is a slow, net 'drift' of electrons in the direction opposite to the electric field. This net average velocity is the drift velocity (v_d). It's a very small velocity, typically of the order of 10⁻⁴ m/s. The relationship is given by v_d = aτ = (-eE/m)τ. This slow drift, when considered for the enormous number of free electrons in a conductor, results in a significant macroscopic current, as described by the equation I = n e A v_d.

Kirchhoff's Laws: A Comparison

Worked Examples

• {"title":"Example 1: Calculating Drift Velocity","bodyMarkdown":"A copper wire of cross-sectional area 2.0 x 10⁻⁶ m² carries a current of 1 A. Given that the number density of free electrons in copper is 8.5 x 10²⁸ m⁻³, calculate the drift velocity of electrons.\n\nSolution:\nWe use the formula: I = n e A v_d\nRearranging for v_d: v_d = I / (n e A)\nGiven: I = 1 A, n = 8.5 x 10²⁸ m⁻³, e = 1.6 x 10⁻¹⁹ C, A = 2.0 x 10⁻⁶ m²\n\nv_d = 1 / (8.5 x 10²⁸ 1.6 x 10⁻¹⁹ 2.0 x 10⁻⁶)\nv_d = 1 / (27.2 x 10³) m/s\nv_d ≈ 3.67 x 10⁻⁵ m/s or 0.0367 mm/s."}
• {"title":"Example 2: Applying Kirchhoff's Loop Rule","bodyMarkdown":"In a simple loop, a cell of EMF 10V and internal resistance 1Ω is connected to an external resistor of 4Ω. Find the current in the circuit and the terminal voltage across the cell.\n\nSolution:\nLet the current in the loop be I. The total resistance is R_total = R_ext + r = 4Ω + 1Ω = 5Ω.\n\nUsing Kirchhoff's Loop Rule (or Ohm's Law for the whole circuit): \nΣε = ΣIR\n10 = I (4 + 1)\n10 = 5I\nI = 10 / 5 = 2 A.\n\nThe current in the circuit is 2 A.\n\nTerminal Voltage (V) across the cell is given by V = ε - Ir.\nV = 10 - (2 1) = 10 - 2 = 8 V.\nThe terminal voltage is 8 V."}

Board Exam Traps and Tips

A very common area for errors is the sign convention in Kirchhoff's Loop Rule. Always fix a direction of traversal for your loop first (clockwise or anti-clockwise).

• When traversing a resistor in the direction of current, the potential change is -IR (potential drop).
• When traversing a resistor opposite to the direction of current, the potential change is +IR (potential gain).
• When traversing a cell from the negative to the positive terminal, the EMF is +ε.
• When traversing a cell from the positive to the negative terminal, the EMF is -ε.

Practice this by drawing simple circuits and applying the rules until it becomes second nature. Double-check your signs before solving the simultaneous equations.

Practice Questions with Solutions

• How does the resistivity of a typical semiconductor (like Silicon) change with an increase in temperature? The resistivity of a semiconductor decreases with an increase in temperature because more charge carriers (electrons and holes) become available for conduction.
• On what principle does a potentiometer work? A potentiometer works on the principle that for a wire of uniform cross-section and composition carrying a constant current, the potential drop across any length of the wire is directly proportional to that length (V ∝ L).
• What happens to the balancing length in a metre bridge experiment if the radius of the bridge wire is doubled? The balancing length remains unchanged. The condition for a balanced Wheatstone bridge (P/Q = R/S) depends on the ratios of resistances, not on the dimensions of the bridge wire itself, as long as it is uniform.
• Why is a high-resistance voltmeter preferred over a low-resistance one for measuring potential difference? A voltmeter is connected in parallel. A high-resistance voltmeter draws negligible current from the main circuit, thus not significantly altering the potential difference it is intended to measure. A low-resistance one would draw a larger current, giving an inaccurate reading.

Frequently Asked Questions

Frequently Asked Questions