CBSE · Class 12 · Physics · Chapter 3

Current Electricity — Formula Sheet

Board Formulas

13 formulas

1.Electric Current
$I = \frac{d q}{d t}$
$I$ : Current (A = C/s) · $q$ : Charge crossing a section (C) · $t$ : Time (s)
Rate of flow of charge. Conventional current is opposite to electron flow.
2.Drift Velocity and Current★
$I = n e A v_{d}$
$n$ : Free-electron density (m⁻³) · $e$ : Electron charge = 1.6×10⁻¹⁹ C · $A$ : Cross-sectional area (m²) · $v_{d}$ : Drift velocity (m/s)
Macroscopic current from microscopic drift of free electrons under an applied field.
3.Drift Velocity in Terms of Field★
$v_{d} = \frac{e E τ}{m}$
Drift velocity is proportional to applied electric field. τ is the relaxation time.
4.Ohm's Law (microscopic form)
$J = σ E, σ = \frac{n e ^{2} τ}{m}$
Current density J is proportional to field E. Conductivity σ depends only on the material.
5.Ohm's Law (macroscopic form)★
$V = I R$
Voltage across a conductor is proportional to current, provided temperature is constant.
6.Resistance of a Uniform Conductor
$R = \frac{ρ L}{A}$
$ρ$ : Resistivity (Ω·m) · $L$ : Length (m) · $A$ : Cross-section area (m²)
Longer conductor ⇒ more resistance. Thicker conductor ⇒ less resistance.
7.Temperature Dependence of Resistivity
$ρ_{T} = ρ_{0} [1 + α (T - T_{0})]$
For metals α > 0 (resistivity rises with T). For semiconductors α < 0.
8.Kirchhoff's Junction Rule (KCL)
$\sum I_{in} = \sum I_{o u t}$
Conservation of charge at any junction — no charge accumulates.
9.Kirchhoff's Loop Rule (KVL)★
$\sum_{l oo p} ε - \sum_{l oo p} I R = 0$
Conservation of energy around a closed loop. Choose direction, be consistent with signs.
10.EMF and Terminal Voltage
$V = ε - I r$
$ε$ : EMF of cell (V) · $r$ : Internal resistance (Ω) · $V$ : Terminal voltage (V)
Terminal voltage V is less than EMF ε when current is drawn from the cell.
11.Wheatstone Bridge Balance★
$\frac{P}{Q} = \frac{R}{S}$
Balance ⇒ no current through galvanometer ⇒ B and D at same potential.
12.Cells in Series and Parallel
$ε_{e q}^{ser i es} = ε_{1} + ε_{2}, \frac{ε _{e q}}{r _{e q}} = \frac{ε _{1}}{r _{1}} + \frac{ε _{2}}{r _{2}} (p a r a l l e l)$
Series: EMFs add, internal resistances add. Parallel: use the reciprocal-like formula for identical cells (r_eq = r/n).
13.Electric Power
$P = V I = I^{2} R = \frac{V ^{2}}{R}$
Three equivalent forms — pick the one avoiding the unknown quantity.