Current Electricity Class 12 Chapter Notes

Key Terms & Definitions

Electric Current (I)

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

Drift Velocity (vd)

The average velocity attained by charged particles (e.g., electrons) in a material due to an electric field. It's typically very small (mm/s).

Relaxation Time (τ)

The average time between two successive collisions of an electron with the positive ions in the conductor.

Ohm's Law

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

Resistance (R)

The opposition offered by a conductor to the flow of electric current. Its SI unit is Ohm (Ω).

Resistivity (ρ)

The intrinsic property of a material that quantifies how strongly it resists electric current. It's independent of the conductor's dimensions. R = ρL/A, so ρ = RA/L. Its SI unit is Ohm-metre (Ωm).

Conductivity (σ)

The reciprocal of resistivity, representing a material's ability to conduct electricity. σ = 1/ρ. Its SI unit is Siemens per metre (S/m).

Electromotive Force (EMF)

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

Kirchhoff's First Law (Junction Rule)

States that the algebraic sum of currents entering a junction (or node) in an electrical circuit is equal to the algebraic sum of currents leaving it. It's based on the conservation of charge.

Kirchhoff's Second Law (Loop Rule)

States that the algebraic sum of changes in potential around any closed loop in an electrical circuit is zero. It's based on the conservation of energy.

Drift Velocity, Mobility, and Microscopic Ohm's Law

In a conductor, electrons are in random motion due to thermal energy. When an electric field (E) is applied, these free electrons experience a force and accelerate. However, they frequently collide with positive ions of the conductor, losing their gained energy. As a result, they acquire a small average velocity in a direction opposite to the electric field, known as drift velocity (vd). This drift velocity is responsible for electric current.

The relationship between drift velocity and electric field is given by: vd = - (eEτ / m), where 'e' is the charge of an electron, 'E' is the electric field, 'τ' is the relaxation time, and 'm' is the mass of an electron. The negative sign indicates that drift velocity is opposite to the electric field.

From the drift velocity, we can establish the relation for current (I): I = n e A vd, where 'n' is the number density of free electrons, 'A' is the cross-sectional area of the conductor. Substituting the expression for vd:

I = n e A (eEτ / m) = (n e² τ / m) A E

Now, let's connect this to Ohm's Law. We know J = I/A (current density) and E = V/L for a conductor of length L. So, J = (n e² τ / m) E.

The term (n e² τ / m) is the conductivity (σ) of the material. Therefore, we get the microscopic form of Ohm's Law: J = σ E.

The mobility (μ) of charge carriers is defined as the magnitude of drift velocity per unit electric field: μ = |vd / E| = (eτ / m). This parameter is useful in understanding the behavior of semiconductors. A higher mobility indicates that charge carriers can move more freely through the material under the influence of an electric field, leading to better conductivity. This fundamental understanding provides a microscopic basis for Ohm's law and helps explain how materials conduct electricity.

Key Formulas and Must-Remember Concepts

• Current (I): I = dQ/dt = n A e vd. (n = number density of electrons, A = area, e = charge, vd = drift velocity)
• Ohm's Law: V = I R (for ohmic conductors).
• Resistance (R): R = ρL/A. Temperature dependence: R_T = R_0[1 + α(T - T_0)]. (α is temperature coefficient of resistance)
• Resistivity (ρ): ρ = m / (n e² τ). Conductivity σ = 1/ρ.
• Series Combination of Resistors: R_eq = R_1 + R_2 + ... (Current is same, voltage divides).
• Parallel Combination of Resistors: 1/R_eq = 1/R_1 + 1/R_2 + ... (Voltage is same, current divides).
• Cells (EMF ε, Internal Resistance r): Terminal potential difference V = ε - Ir (during discharge) or V = ε + Ir (during charging).
• Kirchhoff's Laws: Junction Rule (conservation of charge), Loop Rule (conservation of energy). Crucial for complex circuits.
• Wheatstone Bridge: Balanced condition R_1/R_2 = R_3/R_4. No current flows through the galvanometer arm.
• Potentiometer: Used to compare EMFs (ε_1/ε_2 = L_1/L_2) and find internal resistance of a cell (r = R((L_1/L_2) - 1)). Principle: potential drop across a wire is proportional to its length for uniform current.
• Electric Power (P): P = V I = I²R = V²/R. Joule's Law of Heating: H = I²Rt (Heat produced).

Series vs. Parallel Combination of Resistors

Worked Examples

• {"title":"Example 1: Equivalent Resistance","problem":"Calculate the equivalent resistance of three resistors, 2Ω, 3Ω, and 6Ω, when connected (a) in series and (b) in parallel.","solution":"(a) In series: R_eq = 2Ω + 3Ω + 6Ω = 11Ω.\n(b) In parallel: 1/R_eq = 1/2Ω + 1/3Ω + 1/6Ω = (3+2+1)/6Ω = 6/6Ω = 1/1Ω. So, R_eq = 1Ω."}
• {"title":"Example 2: Power Dissipation","problem":"A light bulb is rated 100W at 220V. Calculate the current drawn and its resistance.","solution":"Given P = 100W, V = 220V.\nCurrent I = P/V = 100W / 220V = 0.45 A (approx).\nResistance R = V²/P = (220V)² / 100W = 48400 / 100 = 484Ω."}

Exam Tip: Avoiding Common Traps

When applying Kirchhoff's Loop Rule, be extremely careful with sign conventions. Always assign a direction for traversing the loop and consistently follow it. Potential drops (e.g., across a resistor in the direction of current) are negative, and potential rises (e.g., going from negative to positive terminal of a cell) are positive. Another common mistake is confusing EMF with terminal potential difference; remember, terminal potential difference is less than EMF when current is drawn from the cell due to internal resistance (V = ε - Ir). For Potentiometer problems, ensure you understand the balancing condition and how the potential gradient works, as diagrams can often be tricky.

Practice Questions with Solutions

• Q: Differentiate between drift velocity and the random thermal speed of electrons in a conductor. A: Drift velocity is the small average velocity in one direction due to an electric field (mm/s), while random thermal speed is much higher (10^5 m/s) and random, leading to zero net current in the absence of an E-field.
• Q: Why is the terminal voltage of a cell less than its EMF when supplying current? A: When a cell supplies current (discharges), there is a potential drop across its internal resistance (Ir). So, the terminal voltage V = EMF - Ir, making it less than the EMF.
• Q: State the principle behind Kirchhoff's Junction Rule. A: Kirchhoff's Junction Rule (KCL) is based on the principle of conservation of electric charge. It states that charge cannot accumulate at any junction; thus, the total current entering a junction must equal the total current leaving it.
• Q: How does the resistivity of a good conductor and a semiconductor change with an increase in temperature? A: For a good conductor, resistivity generally increases with temperature because increased thermal vibrations hinder electron flow. For a semiconductor, resistivity generally decreases with temperature because more charge carriers (electrons and holes) become available due to increased thermal energy.

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