Overview
This lecture covers the complete chapter of Current Electricity, including fundamental definitions, key formulas, Ohm's Law, resistivity, series and parallel circuits, Wheatstone bridge, internal resistance, practical applications, and problem-solving strategies for physics exams.
Basics of Electricity and Electric Current
- Electricity is energy produced by moving charges (electrons or ions).
- Electric current (I) is the flow of charge per unit time: ( I = \frac{dq}{dt} ).
- SI unit of current is ampere (A); 1 A = 1 coulomb/second.
- Conventional current flows from positive to negative; electronic current (electron flow) is in the opposite direction.
EMF and Potential Difference
- Electromotive force (emf, E) is the maximum potential difference provided by a source.
- ( E = \frac{\text{Work done}}{\text{Unit charge}} )
- SI unit for emf and potential difference is volt (V); 1 V = 1 Joule/Coulomb.
- EMF is potential difference across terminals when no current is drawn.
Ohm’s Law and Resistance
- Ohm’s Law: ( V = IR ), current through a conductor is directly proportional to applied potential difference if temperature and dimensions are constant.
- Resistance (R) opposes current flow: ( R = \frac{V}{I} ).
- SI unit of resistance is ohm (Ω); 1 Ω = 1 V/A.
Factors Affecting Resistance & Resistivity
- ( R \propto L/A ) (R increases with length L; decreases with cross-sectional area A).
- ( R = \rho \frac{L}{A} ), where ρ (rho) is resistivity.
- Resistivity depends on material and temperature; unit is Ω·m.
- Conductors have low resistivity, insulators high, semiconductors intermediate.
- For conductors, resistivity increases with temperature: ( \rho_2 = \rho_1[1 + \alpha(T_2 - T_1)] ).
Current Density, Conductance, and Conductivity
- Current density (J): current per unit area, ( J = \frac{I}{A} ).
- Conductance (G) is reciprocal of resistance: ( G = \frac{1}{R} ), unit: S (siemens).
- Conductivity (σ) is reciprocal of resistivity: ( \sigma = \frac{1}{\rho} ), unit: S/m.
Drift Velocity and Mobility
- Drift velocity (v_d) is average velocity of charge carriers under electric field.
- ( v_d = \frac{-eE\tau}{m} ), where τ = relaxation time, m = mass, E = electric field.
- Current: ( I = nAvev_d ); n = number density of electrons.
- Mobility (μ): drift velocity per unit electric field, ( \mu = \frac{v_d}{E} ).
Series and Parallel Circuits
- In series: ( R_{eq} = R_1 + R_2 + ... ), current is same, voltage divides.
- In parallel: ( \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + ... ), voltage same, current divides.
Heating Effects and Power
- Joule’s law: Heat produced, ( H = I^2Rt ).
- Electric power: ( P = VI = I^2R = \frac{V^2}{R} ), unit: Watt (W).
- Energy consumption (commercial unit): kilowatt-hour (kWh); 1 kWh = 3.6 × 10⁶ J.
Internal Resistance & EMF of Cells
- Real cells have internal resistance (r); total resistance is R (external) + r (internal).
- ( E = V + Ir ), ( V = E - Ir ).
- For cells in series: ( E_{tot} = E_1 + E_2 + ... ), ( R_{tot} = R_1 + R_2 + ... ).
- For cells in parallel: ( E_{tot}/R_{tot} = E_1/R_1 + E_2/R_2 + ... ).
Kirchhoff's Laws & Applications
- Kirchhoff's Current Law (KCL): sum of currents entering a junction = sum leaving.
- Kirchhoff's Voltage Law (KVL): total potential drop in a loop equals total emf in that loop.
- Used to analyze complex circuits and networks.
Wheatstone Bridge and Meter Bridge
- Wheatstone bridge: arrangement of 4 resistors; bridge is balanced when ( \frac{P}{Q} = \frac{R}{S} ), no current through galvanometer.
- Used to determine unknown resistance.
Superconductivity
- At critical temperature, resistance of certain materials drops to zero.
- Meissner effect: expulsion of magnetic field from superconductor.
Key Terms & Definitions
- Electric current (I) — rate of flow of charge, I = dq/dt.
- Electromotive force (emf, E) — maximum potential difference a source can provide.
- Potential difference (V) — work needed to move charge between two points.
- Resistance (R) — opposition to current.
- Resistivity (ρ) — resistance per unit length and area.
- Current density (J) — current per unit area, J = I/A.
- Drift velocity (v_d) — average velocity of charge carriers due to electric field.
- Mobility (μ) — drift velocity per unit electric field.
- Conductance (G) — reciprocal of resistance.
- Conductivity (σ) — reciprocal of resistivity.
- Internal resistance (r) — resistance inside a cell or battery.
Action Items / Next Steps
- Revise key formulas and graphs (especially V-I curves).
- Practice solving sample numericals, especially on series/parallel circuits and Wheatstone bridge balancing.
- Complete any assigned MCQs or theory questions from the lecture as homework.
- Prepare summary notes on Kirchhoff’s laws and their applications in circuit analysis.
- Next topic: Crutch/Kirchhoff’s Laws, Wheatstone Bridge, and more exam-oriented problem-solving.