Current Electricity - Short Notes

Electrostatic vs. Current Electricity

• Electrostatic: Charges in rest.
• Current: Charges in motion with velocity.
• Direction of current opposite to that of electron flow.
• Potential difference induces an electric field → causes acceleration → produces drift velocity.
• Drift velocity: Slow velocity caused by electric field (vd = aτ).

Basic Concepts

• Electric current (I): Rate of flow of electric charge.
  • Formula: I = ΔQ / ΔT (Charge/Time).
  • Unit: Ampere (A) → Coulomb/second.
  • Direction: Positive charge flow or opposite to electron flow.
• Instantaneous current: I = dQ/dT.
• Average current: I_average = ∫idt / ∫dt.
• Charge and current relation:
  • If current is a function of time, area under current vs. time graph gives charge.
• Circular motion: I = QV/2πR.

Drift Velocity and Related Formulas

• Drift velocity (vd):
  • Formula: vd = eEτ/m.
• Mobility (μ): Ability of electron to move in conductor.
  • Formula: μ = vd / E.
  • Inversely proportional to mass.
• Current relationship: I = nAve.
  • mnemonic: Vena.
• Current density (J): Vector quantity, J ∝ 1/A.

Resistance

• Ohm's Law: V = IR.
  • Resistors in series: R_eq = R1 + R2 + R3.
  • Resistors in parallel: 1/R_eq = 1/R1 + 1/R2 + 1/R3.
• Resistance dependence: Depends on physical properties (area, length, temperature, resistivity).
• Resistivity (ρ): ρ = m/nτe².
• Effect of temperature: Different for materials (metals, semiconductors, alloys).

Important Devices

• Meter Bridge: Based on Wheatstone bridge principle.
• Potentiometer: Used to measure EMF, internal resistance.

Kirchhoff’s Laws

• KCL: Sum of currents at junction = 0 (conservation of charge).
• KVL: Sum of EMF and potential drops in closed loop = 0.
  • Use sign conventions for potential drops and EMF changes.

Power and Energy

• Power: P = VI.
• Energy lost in resistor: E = I²Rt, E = ∫i²Rdt (for variable current).
• Battery charging/discharging:
  • Charging: Power gained = VI.
  • Discharging: Power lost = VI.