Current Electricity - Important Formulas Table

 Current Electricity - Important Formulas Table

S.No.	Concept / Quantity	Formula	Key Notes
1	Ohm’s Law	$V = IR$	R = Resistance
2	Resistance of Wire	$R = \rho \frac{l}{A}$	ρ = Resistivity
3	Resistivity / Temperature Dependence	$\rho = \rho_0 (1 + \alpha \Delta T)$	α = Temperature coefficient
4	Current Density	$J = \frac{I}{A} = \sigma E$	σ = Conductivity
5	Drift Velocity	$v_d = \frac{e E \tau}{m} = \frac{I}{n e A}$	n = number density of electrons
6	Equivalent Resistance (Series)	$R_{eq} = R_1 + R_2 + \dots$	-
7	Equivalent Resistance (Parallel)	$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$	-
8	Kirchhoff’s Current Law (KCL)	$\sum I_{\text{in}} = \sum I_{\text{out}}$	Junction rule
9	Kirchhoff’s Voltage Law (KVL)	$\sum V = 0$ (Closed loop)	Loop rule
10	EMF of Cell	$\mathcal{E} = V + Ir$	V = Terminal voltage
11	Cells in Series	$\mathcal{E}_{eq} = \mathcal{E}_1 + \mathcal{E}_2$, $r_{eq} = r_1 + r_2$	-
12	Cells in Parallel	$\mathcal{E}_{eq} = \mathcal{E}$, $\frac{1}{r_{eq}} = \frac{1}{r_1} + \frac{1}{r_2}$	Same EMF
13	Wheatstone Bridge (Balanced)	$\frac{P}{Q} = \frac{R}{S}$	No current in galvanometer
14	Meter Bridge / Slide Wire Bridge	$\frac{R}{X} = \frac{l_1}{l_2}$	-
15	Potentiometer (Comparison of EMFs)	$\frac{\mathcal{E}_1}{\mathcal{E}_2} = \frac{l_1}{l_2}$	Null deflection method
16	Potentiometer (Internal Resistance)	$r = R \left( \frac{l_1}{l_2} - 1 \right)$	-
17	Power Dissipated in Resistor	$P = I^2 R = \frac{V^2}{R} = VI$	Three equivalent forms
18	Electrical Energy	$H = I^2 R t$ (Joule’s Law)	Heat produced
19	RC Circuit (Charging)	$q = q_0 (1 - e^{-t/RC})$, $I = I_0 e^{-t/RC}$	Time constant τ = RC
20	RC Circuit (Discharging)	$q = q_0 e^{-t/RC}$, $I = I_0 e^{-t/RC}$	-

Important Constants & Definitions

• 1 Ampere = 1 Coulomb/second
• Resistivity (ρ) of copper ≈ 1.7 × 10⁻⁸ Ωm
• Temperature coefficient (α) of copper ≈ 0.0039 /°C
• Drift velocity is very small (~ mm/s) compared to speed of electrons.

Note: All formulas are in SI units. These are most important for Class 12 Board Exams, JEE Main & NEET.

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