Electric Current, Charge, Potential Difference, and Electromotive Force

Fundamental Equations and Definitions

  • Electric Current: Rate of flow of electric charge past a point per unit time.

    • Equation: I=QtI = \frac{Q}{t}

    • 1 Ampere (A): Defined as one coulomb of charge passing a given point in a circuit per second (1 A=1 C s−11\,\text{A} = 1\,\text{C}\,\text{s}^{-1}).

  • Number of Electrons and Quantisation of Charge:

    • Equation: Q=neQ = n e

    • Where nn is the number of electrons and e=1.6×10−19 Ce = 1.6 \times 10^{-19}\,\text{C} is the elementary charge of an electron.

  • Volt (V): Defined as one joule of energy transferred or work done per coulomb of charge (1 V=1 J C−11\,\text{V} = 1\,\text{J}\,\text{C}^{-1}).

  • Electrical Power: The rate at which electrical energy is transferred or work is done per unit time.

    • Equation: P=Wt=VIP = \frac{W}{t} = V I

Electromotive Force (emf)

  • Definition: The total energy converted from non-electrical forms into electrical energy per unit charge passing through a source to drive current around a complete circuit.

  • Equation: E=WQE = \frac{W}{Q}

  • Examples:

    • Chemical energy converted into electrical energy in a battery or cell.

    • Mechanical energy converted into electrical energy in a generator or dynamo.

    • Solar light energy converted into electrical energy in a photovoltaic cell.

Potential Difference (p.d.)

  • Definition: The electrical energy converted into other forms of energy (such as thermal energy or light) per unit charge as charge flows between two points in a circuit.

  • Equation: W=QVW = Q V

  • Mechanism and Variations:

    • As charge carriers move through circuit components (such as filament lamps or resistors), electrical potential energy is converted into thermal energy or radiation.

    • The potential difference drops across components relative to their resistance; higher resistance components require more work per unit charge to pass through, causing a greater potential drop across them.

Electron Dynamics: No Applied p.d. vs Applied p.d.

  • No Applied Potential Difference:

    • Free electrons undergo rapid, random thermal motion within the metallic crystal lattice at speeds of around 1×106 m s−11 \times 10^6\,\text{m}\,\text{s}^{-1}.

    • Electron movement is isotropic, meaning as many electrons move in one direction as in the exact opposite direction.

    • There is no net flow of charge, resulting in zero electric current (I=0 AI = 0\,\text{A}).

  • Applied Potential Difference:

    • An electric field is established across the conductor.

    • The electric field exerts an electrostatic force on free electrons, accelerating them toward the positive terminal and giving them kinetic energy.

    • Continuous collisions between accelerating electrons and vibrating lattice atoms transfer energy to the lattice, producing a net directional drift velocity along the conductor and establishing an electric current.