Current Electricity

• Electric Current

  • Definition: Rate of flow of electric charge ($I = \frac{Q}{t}$)
  • Direction: Direction of flow of positive charge (opposite to electrons)
  • SI Unit: Ampere (A)
  • Current Density: Current per unit area ($J = \frac{I}{A}$)

• Ohm's Law

  • Statement: $V \propto I$ at constant physical conditions
  • Formula: $V = IR$
  • Resistance ($R$): Opposition to current flow, measured in Ohms ($\Omega$)
  • Resistivity ($\rho$): Material property ($R = \rho \frac{l}{A}$)
  • Limitations: Ohmic vs. Non-ohmic conductors

• Drift Velocity and Origin of Resistance

  • Free electrons in metals exhibit random thermal motion
  • Drift velocity ($v_d$): Average velocity of electrons under an electric field ($v_d = \frac{eE\tau}{m}$)
  • Relation with Current: $I = nAeAv_d$
  • Mobility ($\mu$): Drift velocity per unit electric field ($\mu = \frac{v_d}{E}$)
  • Temperature dependence:
    • Conductors: Resistance increases with temperature ($\alpha > 0$)
    • Semiconductors: Resistance decreases with temperature ($\alpha < 0$)

• Electrical Energy and Power

  • Work Done: $W = VIt = I^2Rt = \frac{V^2}{R}t$
  • Electric Power: Rate of consumption of energy ($P = VI = I^2R = \frac{V^2}{R}$)
  • SI Unit of Power: Watt (W)

• Combination of Resistors

  • Series Combination
    • Same current flows through each resistor
    • Equivalent Resistance: $R_s = R_1 + R_2 + R_3 + \dots$
  • Parallel Combination
    • Potential difference remains the same across each resistor
    • Equivalent Resistance: $\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots$

• Cells, EMF, and Internal Resistance

  • Electromotive Force (EMF, $\varepsilon$): Maximum potential difference across terminals in open circuit
  • Terminal Potential Difference ($V$): Potential difference when current is drawn ($V = \varepsilon - Ir$)
  • Internal Resistance ($r$): Resistance offered by the electrolyte of the cell
  • Combination of Cells:
    • Series grouping
    • Parallel grouping

• Kirchhoff's Rules

  • Kirchhoff's First Rule (Junction Rule)
    • Based on conservation of charge ($\sum I = 0$)
  • Kirchhoff's Second Rule (Loop Rule)
    • Based on conservation of energy ($\sum \Delta V = 0$)

• Wheatstone Bridge

  • Principle: Null deflection method ($I_g = 0$)
  • Balanced condition: $\frac{P}{Q} = \frac{R}{S}$
  • Used to unknown resistance measurement

• Meter Bridge

  • Practical application of Wheatstone Bridge
  • Formula: $S = R \left(\frac{100 - l}{l}\right)$
  • Used to find unknown resistance and resistivity

• Potentiometer

  • Principle: Potential drop is directly proportional to length for uniform wire ($V \propto l$)
  • Advantages over Voltmeter: Measures accurate EMF (infinite resistance at null point)
  • Applications:
    • Comparison of EMFs of two cells ($\frac{\varepsilon_1}{\varepsilon_2} = \frac{l_1}{l_2}$)
    • Determination of internal resistance of a primary cell ($r = R\left(\frac{l_1 - l_2}{l_2}\right)$)