Current Electricity Concepts

Current Electricity

• Electric Current: The rate of flow of electric charge in a definite direction through any cross-section.
• Intensity (Current): Current (I) = Charge (Q) / Time (T). SI unit: Ampere (A), where 1 A = 1 Coulomb/second.
• Charge Carriers:
• Metal: Free electrons
• Electrolyte: Ions
• Gases: Free electrons and ions
• Current Density (J): Defined as the current flowing per unit area held normal to the flow of charge. It's a vector quantity, with direction same as direction of flow of positive charge. J = I / A, or J = I cosθ / A.
• Drift Velocity: The average velocity of free electrons with which they are attracted towards the positive end of a conductor. Order of drift velocity in a conductor is ~10^-4 m/s. The Order of Thermal Velocity is ~10⁵ m/s.
• Relaxation Time: The time between two successive collisions of electrons.
• Temperature increases → Relaxation time decreases
• Mobility: The drift velocity obtained per unit electric field, M = v_d / E.
• Ohm's Law: Current flowing in a conductor is directly proportional to the potential difference (voltage) across its ends, provided that physical conditions, like temperature, remain constant. V α I; V = IR; where R is Resistance.
• Resistance: Obstruction offered in the path of current due to collisions between electrons and ions.
• Resistivity (ρ): Resistance of a unit volume of a conductor. ρ = R(A/L). Units: ohm-meter (Ωm). Resistivity depends only on the material and temperature of the substance.
• Conductance (G): Reciprocal of Resistance, G=1/R, units: siemens (S).
• Effect of Changing Dimensions on Resistance:
• Resistance (R) is directly proportional to length (L)
• Resistance (R) is inversely proportional to cross-sectional area (A)
• Slope of VI Graph: Slope of the V-I graph is equal to Resistance (R).
• Slope of IV Graph: Slope of the I-V graph is equal to 1/Resistance (1/R).
• Effect of temperature on Resistors:
• Temperature increases → Resistance increases for Metals (Temperature coefficient is positive)
• For Alloys like Constantan, Manganin, Nichrome the effect is much smaller, making them suitable for current measuring instruments and other applications
• Temperature increases → Resistance Decreases for Semi-conductors (Temperature coefficient is negative)
• Temperature increases → Resistance decreases for Electrolytes
• Electromotive Force (EMF): Energy required by a charge to complete its cycle in a cell. (Not a force). The maximum potential difference between terminals of a cell in open circuit.
• Terminal Voltage (V): Potential difference across the terminals of a cell when a current is flowing. V = E - Ir, E =emf.
• Internal Resistance: Resistance offered to the flow of ions in the electrolyte of a cell.
• Concentration increases → Internal resistance increases
• Temperature increases → Internal resistance decreases
• Separation between electrodes increases → Internal resistance increases
• Short Circuit: When R = 0, I = E/r, I_max = E/r.
• Series Combination of Cells: I = ne/(R+nr)
• Parallel Combination of Cells: I = ne/(r+mR)
• Kirchhoff's Rules:
• Current Law (Junction Rule): Sum of currents entering a junction equals the sum of currents leaving it.
• Voltage Law (Loop Law): Sum of voltage drops around a closed loop is zero.
• Electric Power: The rate at which electrical energy is dissipated, P = VI = I²R = V²/R. Units: Watts (W).
• Electrical Energy: Energy consumed, E = Pt = I²Rt = V²t/R. Units: Joules (J).
• Power rating: The power that is marked on devices of a given voltage.
• Heating effect: Heating = I²Rt.