Overview
This lecture covers the fundamentals of current electricity, including definitions, key formulas, Ohm's Law, resistance and resistivity, drift velocity, internal resistance, Kirchhoff's laws, Wheatstone bridge, and related problem-solving strategies.
Electric Current: Basics
- Electric current (I) is the rate of flow of free charges through a conductor: I = Q/t.
- SI unit of current is ampere (A), also written as coulomb per second (C/s).
- For non-uniform charge flow, instantaneous current: I = dQ/dt.
- Current flows from high to low potential (conventional current); electrons move in the opposite direction (electronic current).
Conductors, Insulators, and Semiconductors
- Conductors have free electrons and allow easy flow of current (e.g., copper, silver).
- Insulators lack free electrons and do not conduct current.
- Semiconductors conduct current less efficiently and behavior is covered in depth in later chapters.
Ohm’s Law & Resistance
- Ohm’s Law: V = IR; current is directly proportional to potential difference at constant temperature, length, and area.
- Resistance (R) is the opposition to current flow: R = ρ(l/A) where ρ is resistivity.
- Resistivity (ρ) is a property of material, SI unit: ohm-meter (Ω·m).
- Resistance increases with length, decreases with area, and depends on material and temperature.
Drift Velocity & Current Density
- Drift velocity (vd) is the average velocity of electrons due to an electric field: vd = (−eEτ)/m.
- Current density (J): J = I/A; SI unit: A/m²; J = σE, where σ is conductivity.
- Mobility (μ): μ = vd/E = eτ/m.
Internal Resistance & Cells
- Real cells have internal resistance (r): Terminal voltage V = E − Ir, where E is emf.
- In series: total emf = nE, total resistance = n(r) + external resistance.
- In parallel: emf remains E, total internal resistance = r/n.
Kirchhoff’s Laws
- Junction Law: Total current entering a junction equals total current leaving it (conservation of charge).
- Loop Law: Sum of voltage gains and drops around any closed loop is zero (conservation of energy).
- Used to solve complex circuits with multiple sources and resistors.
Wheatstone Bridge
- Balanced Wheatstone bridge: (R1/R2) = (R3/R4); no current flows through the bridge.
- Used for accurate measurement of resistance.
Important Formulas and Graphs
- Power: P = VI = I²R = V²/R.
- Heating effect: Heat (H) = I²Rt.
- Variation of resistance with temperature: R = R₀(1 + αΔT) (α = temperature coefficient).
- Conductance (G) = 1/R; Conductivity (σ) = 1/ρ.
Key Terms & Definitions
- Electric current (I) — Flow of electric charges per unit time.
- Resistivity (ρ) — Material property resisting current flow per unit length and area.
- Drift velocity (vd) — Average velocity of electrons due to electric field.
- Mobility (μ) — Ability of charge carriers to move under electric field.
- Junction Law — Total current into a junction equals total current out.
- Loop Law — Sum of potential differences in a loop is zero.
- Wheatstone Bridge — Circuit for precise measurement of resistance.
Action Items / Next Steps
- Practice at least 100 numerical problems on current electricity from textbooks and question banks.
- Complete homework questions provided in your course materials or PDFs referenced in class.
- Review class notes, especially all derivations and formula connections.
- Watch or revisit earlier chapters if concepts feel unclear, maintaining the sequential order for better understanding.