Fundamentals of Current Electricity

Aug 18, 2024

Notes on Current Electricity Lecture

Key Concepts

  • Current Definition: Current is defined as the flow of charge per unit time.

  • Current Formula: The current can be calculated using the formula:

    [ I = \frac{n \cdot e}{t} ]
    where,

    • ( I ) = current
    • ( n ) = number of electrons
    • ( e ) = charge of an electron (approximately ( 1.6 \times 10^{-19} ) coulombs)
    • ( t ) = time in seconds

Current Calculation Example

  • Given: Flow of ( 10^7 ) electrons per second.
  • Calculation:
    • Number of electrons that pass through a lamp in one minute:
      [ n = \frac{I \cdot t}{e} ]
      • If ( I = 300 \times 10^{-3} ) A and ( t = 60 ) seconds, then:
        [ n = \frac{300 \times 10^{-3} \cdot 60}{1.6 \times 10^{-19}} \approx 1.125 \times 10^{16} ]

Charge Flow Calculation

  • When current becomes zero, the charge can be calculated using:

    [ Q = I \cdot t ]

    • Example calculation for charge when current is zero yields ( Q = 5.5 ) coulombs.

Ohm's Law

  • Statement: Current is directly proportional to the potential difference across the ends of a conductor.

  • Formula:

    [ V = I \cdot R ]
    where,

    • ( V ) = voltage
    • ( R ) = resistance

Resistivity

  • Definition: Resistivity is defined as the resistance of a conductor when its length is 1 meter and its cross-sectional area is 1 square meter.

  • Resistance Relation:

    [ R \propto \frac{L}{A} ]
    where,

    • ( L ) = length of the conductor
    • ( A ) = area of cross-section

Series and Parallel Circuits

  • Series Connection: The total resistance in a series circuit is the sum of individual resistances:

    [ R_{total} = R_1 + R_2 + R_3 ]

  • Parallel Connection: The total resistance in a parallel circuit is given by:

    [ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} ]

Kirchhoff's Laws

  • Junction Rule: The total current entering a junction equals the total current leaving the junction.
  • Loop Rule: The algebraic sum of all potential differences in a closed loop is zero.

Conclusion

  • Potentiometer Principle: The potential drop across a conductor is directly proportional to its length.

  • Final Equation for Potentiometer:

    [ E = \frac{R}{R + r} \cdot L ]

  • Resistances and lengths can be utilized to find readings and calibrations in circuits.

Recommended Actions

  • Review Ohm's Law and circuit calculations for practice.
  • Understand the implications of resistivity and how it affects current flow.