Maharashtra State Board · Class 12 · Physics · Chapter 9

Current Electricity — Formula Sheet

Board Formulas

13 formulas

1.Ohm's Law★
$V = I R$
Applies to ohmic conductors at constant temperature. R depends on material and geometry.
2.Resistivity
$R = ρ \frac{l}{A}$
$ρ$ : Resistivity (Ω·m) · $l$ : Length of conductor (m) · $A$ : Area of cross-section (m²)
ρ is material-specific and depends on temperature. l = length, A = area of cross-section.
3.Drift Velocity and Current★
$I = n A e v_{d}$
n = number density of free electrons, v_d = drift velocity. Explains microscopic origin of current.
4.Mobility
$μ = \frac{v _{d}}{E}$
Drift velocity per unit electric field. Unit: m²·V⁻¹·s⁻¹.
5.Conductivity from Mobility
$σ = n e μ$
Reciprocal of resistivity. Higher mobility ⇒ higher conductivity.
6.Temperature Dependence of Resistance
$R_{T} = R_{0} [1 + α (T - T_{0})]$
α = temperature coefficient of resistance. Positive for metals, negative for semiconductors.
7.Kirchhoff's Current Law (KCL)★
$\sum_{j u n c t i o n} I = 0$
Algebraic sum of currents at a junction is zero. Consequence of conservation of charge.
8.Kirchhoff's Voltage Law (KVL)★
$\sum_{l oo p} Δ V = 0$
Algebraic sum of potential differences around a closed loop is zero. Consequence of conservation of energy.
9.Wheatstone Bridge — Balanced Condition★
$\frac{P}{Q} = \frac{R}{S}$
No current through galvanometer at balance. P, Q, R, S are the four arm resistances.
10.Potentiometer Principle★
$ε \propto l \Rightarrow \frac{ε _{1}}{ε _{2}} = \frac{l _{1}}{l _{2}}$
For a uniform wire carrying constant current, potential drop is proportional to length. Compare two EMFs by comparing balancing lengths.
11.Internal Resistance from Potentiometer
$r = R (\frac{l _{1} - l _{2}}{l _{2}})$
l₁ = balancing length with open circuit, l₂ = balancing length when cell shunted by R.
12.Cells in Series and Parallel
$ε_{e q}^{ser i es} = ε_{1} + ε_{2}, \frac{1}{r _{e q}^{p a r a l l e l}} = \frac{1}{r _{1}} + \frac{1}{r _{2}}$
Series adds EMFs; parallel reduces internal resistance.
13.Power Dissipated
$P = V I = I^{2} R = \frac{V ^{2}}{R}$
Three equivalent forms. Choose the one that avoids the unknown.