Current Electricity Overview

Overview

This lecture covers the key concepts of Current Electricity, including definitions, formulas, important laws, and methods for solving numerical problems. It emphasizes understanding electric current, drift velocity, resistance, Ohm's law, electric cells, Kirchhoff’s laws, and Wheatstone Bridge.

Electric Current & Current Density

• Electric current is the rate of flow of electric charge through a conductor.
• Current flows from high to low potential by convention, opposite to electron flow.
• Average current: ( I_{avg} = \Delta Q / \Delta T ); Instantaneous current: ( I = dQ/dt ).
• Direction of conventional current is the direction of positive charge movement.
• SI unit of current is ampere; current is a fundamental scalar quantity.
• Current density (( J )) is current per unit area and is a vector: ( J = I/A ); unit is A/m²._

Drift Velocity, Mobility, and Related Formulas

• In metals, free electrons move randomly unless an electric field is applied.
• Drift velocity (( v_d )) is the average velocity of electrons due to an external electric field.
• ( v_d = -eE\tau/m ), where ( \tau ) is mean relaxation time, ( E ) is electric field.
• Mobility (( \mu )) is drift velocity per unit electric field: ( \mu = v_d/E = e\tau/m ).
• Current: ( I = n e A v_d ); Current density: ( J = n e v_d ).
• Relation with mobility: ( I = n e A \mu E ).

Ohm's Law & Resistance

• Ohm's Law: ( V \propto I ) if temperature and dimensions are constant; ( V = IR ).
• Resistance (( R )) depends on material, length, area: ( R = \rho L/A ).
• Resistivity (( \rho )) depends only on material and temperature, not shape/dimensions.
• Resistance increases with length and decreases with area; ( R \propto L^2 ) if volume is constant and length is stretched.
• Unit of resistance: ohm (Ω), ( 1 \Omega = 1, V/A ).

Conductors, Non-Ohmic Conductors, and Power

• Ohm's law applies only to materials with a linear V-I graph (ohmic conductors).
• Non-ohmic conductors (e.g. diodes, transistors) do not follow Ohm’s law.
• Joule’s Law of Heating: ( H = I^2 R t ).
• Power: ( P = VI = I^2 R = V^2/R ); unit is watt (W).

Resistivity, Conductance & Temperature Dependence

• Resistivity (( \rho )) is resistance of 1m length, 1m² area: ( \rho = R ) for unit dimensions.
• Conductance (( G )) is ( 1/R ); unit is siemens (S).
• Conductivity (( \sigma )) is ( 1/\rho ); unit S/m.
• For conductors, resistance and resistivity increase with temperature: ( R_T = R_0(1+\alpha \Delta T) ).
• For semiconductors, resistance/resistivity decrease with temperature.

Electric Cell, EMF, and Internal Resistance

• A cell converts chemical to electrical energy.
• EMF is the maximum potential difference across a cell with no current drawn.
• Terminal potential difference is lower than EMF when current flows: ( V = E - Ir ) (discharging), ( V = E + Ir ) (charging).
• Internal resistance increases with electrode distance/concentration, decreases with area/temperature.

Combination of Cells

• Series: ( I = nE/(R + nr) ) where n = number of cells.
• Parallel: ( I = E/(R + r/n) ).
• Mixed: ( I = mnE/(mR + nr) ) for m rows with n cells each.
• Maximum current when internal and external resistance are equal.

Kirchhoff’s Laws

• Junction law: Sum of currents entering a junction equals sum leaving (conservation of charge).
• Loop law: Sum of potential differences in a closed loop is zero (conservation of energy).

Wheatstone Bridge

• Used to measure unknown resistance in a balanced bridge.
• Balance condition: ( P/Q = R/S ) or ( R_1/R_2 = R_3/R_4 ).
• No current flows through galvanometer when bridge is balanced.

Key Terms & Definitions

• Electric Current — Rate of flow of electric charge.
• Current Density (J) — Current per unit area (vector).
• Drift Velocity — Average velocity of electrons under electric field.
• Mobility (( \mu )) — Drift velocity per unit electric field.
• Resistance (R) — Opposition to current; ( R = V/I ).
• Resistivity (( \rho )) — Material property, ( \rho = RA/L ).
• Conductance (G) — Reciprocal of resistance, ( G = 1/R ).
• Conductivity (( \sigma )) — Reciprocal of resistivity, ( \sigma = 1/\rho ).
• EMF — Maximum potential difference of a cell at zero current.
• Internal Resistance (r) — Resistance within a cell due to electrolyte.
• Joule’s Law — Heat produced ( H = I^2 R t ).
• Wheatstone Bridge — Circuit for measuring unknown resistance using balance conditions.

Action Items / Next Steps

• Revise the chapter and formulas.
• Solve at least 10 numericals per day from this chapter (target: 60 by next class).
• Be prepared for numericals and conceptual questions on each topic.