Chapter 3: Current Electricity | Summary

In conductors, particularly metals, some electrons are free to move within the bulk material. Without an electric field, electrons undergo thermal motion with random directions, resulting in zero net current. When an electric field is applied, electrons experience a force and drift, producing a net current.

In solid conductors, the current is carried by negatively charged electrons moving against the direction of the electric field. Without a sustained electric field (maintained by cells or batteries), charges quickly neutralise and current ceases. The study focuses on steady currents produced by steady electric fields maintained by external sources.

Ohm's law, discovered by G.S. Ohm in 1828, states that the potential difference V across a conductor is proportional to the current I through it: V = RI, where R is the resistance measured in ohms (Ω). Resistance depends on both the material and dimensions of the conductor.

The resistance of a conductor is directly proportional to its length l and inversely proportional to its cross-sectional area A: R = ρl/A, where ρ is the resistivity of the material. Ohm's law can also be stated in vector form as j = σE, where σ = 1/ρ is the conductivity. This microscopic form relates current density to electric field.

When an electric field is applied to a conductor, electrons accelerate between collisions with fixed ions. After each collision, their velocity direction is random, but they acquire a small net average velocity in the direction opposite to the field, called drift velocity: vd = –eEτ/m, where τ is the relaxation time (average time between collisions).

The drift velocity is surprisingly constant despite the acceleration, because collisions continuously randomise the electron motion. From the drift model, conductivity is derived as σ = ne²τ/m, and resistivity as ρ = m/(ne²τ). This simple model successfully reproduces Ohm's law and provides a physical explanation for resistance in metals.

Mobility μ is defined as the magnitude of drift velocity per unit electric field: μ = |vd|/E = eτ/m. Its SI unit is m²/Vs. Mobility is always positive and is a measure of how easily charge carriers move through a material under an applied field.

Mobility is relevant for all types of charge carriers: electrons in metals, electrons and positive ions in ionised gases, and both positive and negative ions in electrolytes. Higher mobility implies lower resistivity for a given charge carrier density.

Ohm's law is not a fundamental law of nature. It breaks down in materials and devices where the V-I relationship is non-linear, direction-dependent, or non-unique. For example, in a diode, reversing the voltage does not produce a current of equal magnitude in the opposite direction.

GaAs exhibits a non-unique V-I relationship where the same current corresponds to more than one voltage value. Such non-ohmic devices are widely used in electronic circuits. A material obeys Ohm's law only when its resistivity is independent of the magnitude and direction of the applied electric field.

Materials are classified based on their resistivities. Metals have very low resistivities in the range 10⁻⁸ to 10⁻⁶ Ωm. Insulators like ceramic, rubber, and plastics have resistivities up to 10¹⁸ times greater than metals. Semiconductors like silicon and germanium lie in between.

The resistivity of semiconductors decreases with the addition of suitable impurities, a property exploited in electronic devices. Alloys like Nichrome, Manganin, and Constantan have very weak temperature dependence of resistivity, making them ideal for standard wire-wound resistors.

For metallic conductors over a limited temperature range, resistivity varies linearly: ρT = ρ₀[1 + α(T – T₀)], where α is the temperature coefficient of resistivity with unit (Temperature)⁻¹. For metals, α is positive, meaning resistivity increases with temperature.

The increase in metal resistivity with temperature occurs because higher temperatures lead to more frequent electron-ion collisions (smaller τ), while n remains constant. For semiconductors and insulators, n increases with temperature, more than compensating the decrease in τ, so their resistivity decreases with temperature.

When current I flows through a conductor with potential difference V, energy is dissipated as heat at a rate P = IV. Using Ohm's law, this becomes P = I²R = V²/R. This heating effect (Joule heating or ohmic loss) is the mechanism behind devices like electric bulbs and toasters.

For power transmission, the power lost in transmission cables is Pc = P²Rc/V². To minimise transmission losses, power is sent at very high voltages. Transformers are used to step up voltage at the source end and step it down at the consumer end to safe levels.

A cell maintains steady current using chemical energy. It has two electrodes immersed in an electrolyte. The EMF (ε) is the potential difference between positive and negative terminals in open circuit: ε = V₊ + V₋. EMF is not a force but a potential difference, named so for historical reasons.

When current I flows through a cell with internal resistance r, the terminal voltage is V = ε – Ir. The maximum current from a cell is Imax = ε/r (when external resistance R = 0). Internal resistance of dry cells is much higher than that of common electrolytic cells.

For n cells in series, the equivalent EMF is the sum of individual EMFs (with sign depending on orientation), and the equivalent internal resistance is the sum of individual internal resistances. Series combination is useful when higher voltage is required.

For cells in parallel, the equivalent EMF and internal resistance are given by: 1/req = Σ(1/ri) and εeq/req = Σ(εi/ri). Parallel combination reduces internal resistance and is used when higher current capacity is needed from a source.

Kirchhoff's Junction Rule states that the sum of currents entering a junction equals the sum of currents leaving it. This is based on conservation of electric charge, ensuring no accumulation of charge at any point in a steady-state circuit.

Kirchhoff's Loop Rule states that the algebraic sum of potential changes around any closed loop in a circuit is zero. This follows from the fact that electric potential depends only on position, so returning to the same point implies net zero change. Together, these rules allow analysis of any complex circuit.

A Wheatstone bridge consists of four resistors R₁, R₂, R₃, R₄ arranged in a diamond. A battery is connected across one diagonal (battery arm) and a galvanometer across the other (galvanometer arm). When the bridge is balanced (Ig = 0), the null condition is R₁/R₂ = R₃/R₄.

The Wheatstone bridge is used to precisely determine an unknown resistance. By keeping three resistances known and adjusting one (R₃) until the galvanometer shows null deflection, the unknown R₄ = R₃(R₂/R₁). A practical implementation of this principle is the meter bridge.

Current Electricity is a foundational chapter that builds the understanding of how charge flow is governed in conductors. Starting from the microscopic picture of drifting electrons, it establishes Ohm's law and resistivity from first principles, and extends to the behaviour of cells, combinations of resistors, and the powerful analytical tools of Kirchhoff's rules. The interplay between EMF, internal resistance, and external circuits is central to all real-world electrical systems.

This chapter is critically important for the CBSE board exam, contributing questions on Ohm's law, drift velocity, resistivity and its temperature dependence, EMF and terminal voltage, series-parallel cell combinations, and Kirchhoff's rules with Wheatstone bridge applications. Numerical problems, assertion-reasoning, and application-based questions from this chapter appear regularly. A thorough grasp of both the conceptual and mathematical aspects is essential for scoring well.