Electric Current and Conductivity Summary

Electric Current and Conductivity

  • Atom Structure: Smallest unit of material; nucleus with revolving electrons.

    • Valence Electrons: Outermost electrons that become de-localized in metals, facilitating electric current.

  • Electric Current Definition: Rate of flow of charge, denoted as ๐‘ฐ = ๐’’/๐’•.

  • Electrostatics: Study of stationary charges.

  • Current Electricity: Study of moving charges.

  • Current Flow:

    • From positive terminal to negative terminal (conventional current).
    • Electrons flow in the opposite direction.

  • Ohmโ€™s Law:

    • Current (I) is directly proportional to potential difference (V) when physical state is unchanged: ๐‘‰ = ๐ผ๐‘….
    • Resistance (R): Opposition to current flow; unit is Ohm (โ„ฆ).
    • One Ohm = 1 Volt / 1 Ampere.

  • Conductance: Reciprocal of resistance (C = 1/R); SI unit is Siemens (S).

  • Ohmic Devices: Devices that obey Ohm's law (e.g., copper wire).

  • Non-Ohmic Devices: Do not obey Ohm's law (e.g., diodes, vacuum tubes).

Electrical Energy and Power

  • Energy Work Relationship:

    • Electric potential V = Work done W / Charge Q, where ( W = VQ ).

  • Electric Power (P): Rate of energy transfer, ( P = / t = VI ).

  • SI Unit of Power: Watt (W).

    • 1 hp = 746 W.
    • 1 unit of electricity = 1 kW-h.

  • Resistors:

    • Used to limit current. Types include Carbon resistors and Wire wound resistors.
    • Resistors are color-coded for their resistance values (standardized by EIA).

Resistor Combinations

  • Series Combination:

    • Same current flows through each resistor.
    • Total Resistance: ๐‘…๐‘ก = ๐‘…โ‚ + ๐‘…โ‚‚ + โ€ฆ + ๐‘…๐‘›.

  • Parallel Combination:

    • Potential difference remains the same; current splits across resistors.
    • Total Resistance: ( 1/Rt = 1/Rโ‚ + 1/Rโ‚‚ + โ€ฆ + 1/Rn ).

Specific Resistance (Resistivity)

  • Dependence: Resistance increases with length of conductor, decreases with area of cross-section.
    • ( R = \rho (l/A) ), where ฯ is resistivity (unit: Ohm-meter). Conductivity (ฯƒ) is the reciprocal of resistivity.

Temperature Effects

  • Resistivity Variation with Temperature:
    • Directly proportional increase in resistivity with temperature rise: ( \rho - \rhoโ‚€ = \alpha \rhoโ‚€ (T - Tโ‚€) ).
  • Temperature Coefficient of Resistivity (ฮฑ): ( \text{Unit: } K^{-1} ).

Electromotive Force (EMF) and Internal Resistance

  • EMF Definition: Energy supplied by the cell to drive unit charge around a circuit: ( E = W/q ).
  • Internal Resistance (r): Resistance offered by the cell when current flows.
    • EMF is less than the terminal voltage due to internal resistance.

Cells in Series and Parallel

  • Series Connection:

    • Higher resultant voltage. Current remains the same.
    • Total voltage: ( V = E1 + E2 - I(r1 + r2) ).

  • Parallel Connection:

    • Voltage remains the same while current increases.
    • Total voltage not increased by adding more cells.

Types of Electrical Cells

  • Primary Cell: Non-rechargeable (e.g., dry cells).
  • Secondary Cell: Rechargeable (e.g., lead-acid batteries, solar cells).
  • Fuel Cell: Environment-friendly electric vehicles using hydrogen as fuel, emitting only water as a byproduct.