Current Electricity

The One Thing

Current Electricity links the microscopic drift of charge carriers to measurable circuit quantities such as current, potential difference, resistance, and power. Circuit behaviour is analysed using Ohm’s law, resistance relations, Kirchhoff’s rules, and Wheatstone-bridge balance, each subject to specified physical conditions.

Reactions, Processes and Experiments

Key Terms

• Electric current: The rate of flow of electric charge through a cross-section of a conductor. It is given by I = dQ/dt and measured in amperes (A).
• Conventional current: The assumed direction of current from higher potential to lower potential, opposite to electron drift in a metallic conductor.
• Drift velocity: The average velocity acquired by free electrons because of an applied electric field; for electrons, it is opposite to the electric-field direction.
• Current and drift velocity relation: For a metallic conductor, I = nAevd, where n is charge-carrier number density, A is cross-sectional area, e is electronic charge, and vd is drift velocity.
• Current density: Current per unit cross-sectional area, given by J = I/A = nevd.
• Ohm’s law: At constant temperature and other physical conditions, potential difference is directly proportional to current: V = IR.
• Ohmic conductor: A conductor that obeys Ohm’s law under specified constant physical conditions.
• Resistance: The opposition offered by a conductor to current flow, defined by R = V/I; its SI unit is the ohm (Ω).
• Resistivity: The resistance of a material sample of unit length and unit cross-sectional area, given by ρ = RA/L; its SI unit is ohm metre (Ω m).
• Conductivity: The ability of a material to conduct current, given by σ = 1/ρ.
• Mobility: Drift velocity acquired per unit electric field, given by μ = vd/E; conductivity is related to mobility by σ = neμ.
• Temperature dependence of resistance: For many metallic conductors over a limited range, resistance varies approximately as R_T = R_0[1 + α(T - T_0)].
• Temperature coefficient of resistance: The quantity α in the temperature relation for resistance.
• Series combination of resistors: A connection in which resistors carry the same current; R_s = R_1 + R_2 + R_3 + ....
• Parallel combination of resistors: A connection in which resistors have the same potential difference; 1/R_p = 1/R_1 + 1/R_2 + 1/R_3 + ....
• Electromotive force: Energy supplied by a source per unit charge in moving charge through the complete circuit; it is denoted by ε and measured in volts.
• Internal resistance: Resistance within a cell or source that causes a potential drop when current flows.
• Terminal potential difference: The potential difference across a cell’s terminals; for a discharging cell, V = ε - Ir, and for a charging cell, V = ε + Ir.
• Kirchhoff’s junction rule: The algebraic sum of currents at a junction is zero, expressing conservation of charge.
• Kirchhoff’s loop rule: The algebraic sum of potential changes around a closed loop is zero, expressing conservation of energy.
• Wheatstone bridge: A four-resistance network used to determine an unknown resistance by comparison with known resistances.
• Balanced Wheatstone bridge: A bridge in which no current flows through the galvanometer; for arms P, Q, R, and S, balance requires P/Q = R/S.
• Metre bridge: A practical Wheatstone bridge using a uniform one-metre resistance wire; at balance, X/R = l/(100 - l).
• Electrical energy: Energy supplied or consumed in a circuit, given by W = VIt.
• Electrical power: The rate of electrical energy transfer, given by P = VI = I^2R = V^2/R; its SI unit is the watt.
• Kilowatt-hour: A commercial unit of electrical energy equal to 3.6 × 10^6 J.

Easily Confused

• Conventional current and electron drift: Conventional current is taken from higher to lower potential, whereas electrons drift in the opposite direction.
• Resistance and resistivity: Resistance depends on a particular conductor’s material, length, cross-sectional area, and temperature; resistivity is an intrinsic material property at a specified temperature.
• Ohmic and non-ohmic conductors: An ohmic conductor gives a straight-line V–I graph through the origin under constant conditions; diodes and filament lamps may be non-ohmic.
• Series and parallel combinations: Series resistors carry the same current and have voltage division; parallel resistors have the same potential difference and current division.
• Emf and terminal potential difference: Emf is the energy supplied per unit charge by the source, whereas terminal voltage is affected by internal resistance and current.
• Kirchhoff’s junction and loop rules: The junction rule expresses conservation of charge; the loop rule expresses conservation of energy.
• Wheatstone bridge and metre bridge: A metre bridge is a practical Wheatstone bridge using a uniform one-metre resistance wire.
• Resistance and conductance: Resistance opposes current and is measured in ohms; conductivity describes a material’s ability to conduct and is the reciprocal of resistivity.

What Gets Asked

• Define electric current and use I = Q/t or I = dQ/dt; marks are lost by confusing steady-current and time-varying-current expressions.
• Explain metallic conduction using drift velocity and apply I = nAevd or J = I/A = nevd; marks are lost by treating electron drift as occurring in the conventional-current direction.
• Apply Ohm’s law, identify an ohmic conductor from a straight-line V–I graph through the origin, and interpret the slope as resistance; marks are lost by treating Ohm’s law as universal for devices such as diodes and filament lamps.
• Calculate resistance, resistivity, conductivity, mobility, or temperature-dependent resistance using R = ρL/A, ρ = RA/L, σ = 1/ρ, μ = vd/E, σ = neμ, and R_T = R_0[1 + α(T - T_0)]; marks are lost by treating resistance and resistivity as interchangeable.
• Determine currents, terminal voltage, and power in series, parallel, or source circuits; marks are lost by omitting internal resistance or using V = ε - Ir for a charging cell, where V = ε + Ir applies.
• Apply Kirchhoff’s rules or calculate an unknown resistance using a balanced Wheatstone bridge or metre bridge; marks are lost by using the wrong conservation principle, omitting the zero galvanometer current at balance, or misusing X/R = l/(100 - l).