Current Electricity Formula Sheet

Current Electricity - Formula Sheet

Electric Current: I = q / t (for steady flow) or I = dQ / dt (instantaneous). Units: Ampere (A).
Drift Velocity: v_d = (eτ/m)E = μE. Here e is electron charge, τ is mean free time, m is electron mass, and μ is mobility.
Current Density: J = I / A = n e v_d. Here n is free electron density.
Microscopic Ohm's Law: J = σ E. Here σ is electrical conductivity.
Macroscopic Ohm's Law: V = IR. V is potential difference, I is current, R is resistance.
Resistance: R = ρ (l / A). ρ is resistivity, l is length, A is cross-sectional area.
Temperature Dependence: R_T = R₀[1 + α(T - T₀)]. α is the temperature coefficient of resistance.
Electric Power: P = VI = I²R = V² / R. Measured in Watts (W).
Electric Energy: E = Pt = VIt. Measured in Joules (J) or kWh (1 kWh = 3.6 x 10⁶ J).
Series Resistance: R_s = R₁ + R₂ + ... + R_n.
Parallel Resistance: 1/R_p = 1/R₁ + 1/R₂ + ... + 1/R_n.
Cells in Series (Total Current): I = nε / (nr + R). n is number of cells, ε is emf, r is internal resistance.
Joule's Law of Heating: H = I²Rt. H is the heat produced in a resistor.

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