Current Electricity Formula

Ohm’s Law Formula:

V = I×R

where,

• V = voltage (in volts)
• I = current (in amperes)
• R = resistance (in ohms)

Power Formula:

P = V×I

where,

• P = power (in watts)
• V = voltage (in volts)
• I = current (in amperes)

Resistivity Formula:

R = ρ × {l\over a}

where,

• R = resistance (in ohms)
• ρ = resistivity (in ohm-meter)
• l = length of the conductor (in meters)
• a = cross-sectional area of the conductor (in square meters)

Conductance:

G = 1\over R

• G: Conductance (in siemens or mho)
• R: Resistance (in ohms)

Drift velocity:

I = nev_dA

v_d = I \over neA

v_d = at = eEt \over m

• v_d: Drift velocity (in meters per second)
• I: Current (in amperes)
• n: Number density of charge carriers (in per cubic meter)
• e: Charge of an electron (in coulombs)
• A: Cross-sectional area of the conductor (in square meters)
• t: time interval

Current Density:

J = I \over A

J = nqv_d   [since I = nev_dA]

• J: Current density (in amperes per square meter)
• I: Current (in amperes)
• A: Cross-sectional area of the conductor (in square meters)

Series Resistance Formula:

R= R₁ + R₂ + R₃

where,

• R = total resistance in a series circuit
• R₁, R₂, R₃ = individual resistances in the circuit

Parallel Resistance Formula:

{1\over R} = {1\over R_1} + {1\over R_2} + {1\over R_3}

• R = total resistance in a parallel circuit
• R₁, R₂, R₃ = individual resistances in the circuit

EMF and Internal Resistance of a Cell:

V = ε – Ir

I = ε\over R + r

• V = Terminal voltage of the cell (in volts)
• ε = EMF of the cell (in volts)
• I = Current flowing through the circuit (in amperes)
• r = Internal resistance of the cell (in ohms)

Kirchhoff’s Laws:

a) Kirchhoff’s Current Law (KCL):

ΣI_in = ΣI_out

The sum of currents entering a junction is equal to the sum of currents leaving the junction.

b) Kirchhoff’s Voltage Law (KVL):

ΣIR = V

The sum of voltage drops around any closed loop in a circuit is equal to zero.

Wheatstone Bridge Formula:

{R_1\over R_2} = {R_3\over R_4}

where,

R₁, R₂, R₃, R₄ = resistances in a Wheatstone bridge circuit