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.