Electricity and Charge Carriers Quiz

Current carriers: Charged particles create an electric current when moving in a specific direction.

Solids (metals): Electrons are the charge carriers in metallic conductors. Electric current is caused by electron drift.
Liquids (electrolytes): Positive and negative ions are the charge carriers in electrolytic liquids. Examples include Cu²⁺ and SO₄²⁻ ions in CuSO₄ solution.
Gases (ionized): Positive and negative ions and electrons are the charge carriers in ionized gases.

Free electrons: Metals contain a large number of free electrons (approximately 10²⁸ per cubic meter).
Random motion: Without an electric field, these electrons move randomly due to thermal energy.
Average velocity: The average velocity of electrons in any given direction is zero, as many electrons move in the opposite direction.
External field: An external electric field exerts a force on electrons, causing them to accelerate.
Collisions: Electrons frequently collide with metal ions, losing their acquired velocity and starting afresh with thermal velocity.
Drift velocity (vd): The average velocity acquired by electrons in a specific direction due to the electric field. Vd is proportional to the strength of the electric field (E) and inversely proportional to the mass of the electron (m).

Electric current (I): The rate of flow of charge.
Current density (j): Current per unit area.
Formula: I = n e A v_d , where n is the number density of charge carriers, e is the charge of a carrier, A is the cross-sectional area, and v_d is the drift velocity.

Ohm's Law: For a given conductor, voltage (V) is directly proportional to current (I) at a constant temperature.
Resistance (R): The constant of proportionality in Ohm's Law, V = IR.
Resistivity (ρ): Material property describing how strongly a material resists current flow. ρ = m/ n e² τ A, where n is the number density of charge carriers, m is the mass of the electron, τ is the relaxation time, and A is the area.

Resistivity is independent of the dimensions of the conductor.
Resistivity depends on the number of free electrons per unit volume (electron density).
Resistivity depends on the relaxation time (τ), the average time between successive collisions of an electron.

Collisions cause resistance: Electron collisions with positive ions oppose electron flow. This resistance increases with more collisions.
Resistivity and material: Resistance depends on the material arrangement (e.g., copper vs. other metals) as this affects collision frequencies.
Resistance and length: Longer wires offer more resistance.
Resistance and cross-sectional area: Thicker wires have less resistance due to increased area for electron flow

Electrical conductivity: The capability of a material to conduct an electric current.
Mobility (α): The drift velocity gained by a charge carrier in a unit electric field. (α=vd/E)
Formulae: α = v_d/E , α =qτ/m , or α =qEτ/m
Units of mobility: m²/Vs

Definition: The resistance offered by the electrolyte of a cell to the flow of current between its electrodes.
Factors: Depends on the electrolyte's nature, concentration, distance between electrodes, common area and temperature.
Freshly prepared cells: Have low internal resistance. Internal resistance increases as current is drawn.

Electromotive force(emf): Energy provided by a cell per unit charge.
Terminal potential difference(pd): The voltage from one end to the other across the external circuit.
Formulae: E = V + Ir ; V = E – Ir

Equivalent emf: The sum of individual emfs, Eeq = E1 + E2 +...+ En.
Equivalent internal resistance: The sum of individual internal resistances, req = r1 + r2 +...+ rn.

Equivalent emf for parallel combination: Eeq= E , where E is the emf of a single cell.
Equivalent internal resistance for parallel combination: req = r1 r2 / (r1 + r2).

Series Connection: For maximum current with a series combination of cells, the external resistance should be higher than the total internal resistance.
Parallel Connection: For maximum current with a parallel combination of cells, the external resistance should be smaller than the reciprocal of the total internal resistance.

Kirchhoff's First Law (Junction Rule): The algebraic sum of currents at any junction in a circuit is zero. The current entering a junction equals the current leaving it. (ΣI=0)
Kirchhoff's Second Law (Loop Rule): The algebraic sum of the potential differences in any closed loop of a circuit is zero. (ΣΔV = 0)

Procedure: Follow the steps for applying Kirchhoff's rules to solve electrical circuit problems and compute the unknown currents/values involved.

Definition: A circuit configuration used to measure an unknown resistance by balancing it against known resistances (P, Q, R).
Formulae: P/Q = R/S
Sensitivity: High sensitivity when the resistances in the arms (P, Q, R, and S) are approximately equal.
Balanced Condition: No current flows through the galvanometer when the bridge is balanced; ensures the null condition.

Definition: A practical application of the Wheatstone bridge, uses a uniform wire with known resistance per unit length.
Principle: Based on Wheatstone bridge principles.
Working: Measures unknown resistance by balancing the bridge using a sliding contact (jockey).