Current Electricity: MDCAT Notes and MCQs

Current

• I = Q/t, ampere (1 A = 1 C s⁻¹). Steady current: constant rate of flow of charge (same magnitude and direction with time). Conventional current flows from + to − (opposite to electrons).
• Drift velocity of electrons is very small (≈ 10⁻³ m s⁻¹) but the signal travels near light speed.

Ohm's law

Current through a conductor is directly proportional to the potential difference across its ends, provided temperature and physical conditions remain constant: V = IR. Ohmic conductors give a straight-line I–V graph; filament lamps, diodes, thermistors are non-ohmic.

Resistivity

• R = ρL/A; resistivity ρ (Ω m) is a property of the material. Conductance G = 1/R (siemens); conductivity σ = 1/ρ.
• Temperature dependence: R_t = R₀(1 + αΔT), ρ_t = ρ₀(1 + αΔT). α = temperature coefficient of resistivity (K⁻¹).
• Metals: α positive — resistance increases with temperature (more lattice vibrations). Semiconductors (Si, Ge), carbon, insulators: α negative. Alloys (manganin, constantan, nichrome): very small α.

EMF & internal resistance

• EMF (E): energy supplied per unit charge by the source (volt). Every real source has internal resistance r.
• Terminal voltage V = E − Ir. V < E when current flows; V = E on open circuit (I = 0). Current I = E/(R + r). Short circuit (R = 0): I = E/r — large current, heating.
• Consequence: as load current increases, terminal voltage drops ("lost volts" Ir).

Maximum power transfer

Power to external load P = I²R = E²R/(R + r)². It is maximum when R = r (load equals internal resistance): P_max = E²/4r. Efficiency at this point is only 50%.