Formula sheet: Current Electricity

Current Electricity14 min readLesson 1 of 6

1.1 Current and drift Current is the rate at which charge crosses a section of a conductor. In a metal the moving charges are electrons, and they drift slowly in the direction opposite to the applied field. The current is large even when the drift speed is tiny, because a conductor contains an enormous number of free electrons. Current density is current per unit area. It is a vector that points in the direction of the current, while current itself is a scalar. The drift velocity connects the microscopic picture to the measured current through the number density of free electrons. Ohm's law holds for many conductors at constant temperature: the current through the conductor is proportional to the potential difference across it. The constant of proportionality is the resistance, and its reciprocal is the conductance. Devices such as diodes do not obey this law, so treat Ohm's law as an observed property of certain materials rather than a law of nature.

I = \frac{d Q}{d t}, J = \frac{I}{A} = n e v_{d}

Current and current density in a conductor with n free electrons per unit volume

v_{d} = \frac{e E τ}{m}

Drift velocity in terms of relaxation time tau

V = I R, R = \frac{ρl}{A}

Ohm's law and the resistance of a wire of length l and area A

σ = \frac{1}{ρ} = \frac{n e ^{2} τ}{m}

Conductivity from the free electron model

1.2 Cells and circuits A cell maintains a potential difference between its terminals by converting chemical energy into electrical energy. Its electromotive force is the potential difference across the terminals when no current is drawn. When current flows, the terminal voltage is smaller than the emf because of the internal resistance of the cell. Kirchhoff's rules extend Ohm's law to networks that cannot be reduced by simple series and parallel steps. The junction rule follows from conservation of charge, and the loop rule follows from conservation of energy. Use them together for multi-loop circuits. Quantity Expression Note Terminal voltage of a cell emf minus I r r is the internal resistance Two cells in series emfs add, resistances add same current through both Two cells in parallel emf and r from the parallel formulas used when currents divide Wheatstone balance P/Q = R/S galvanometer carries no current Potentiometer balance emf proportional to balancing length null method, no current drawn 1.3 Units that must line up Current in ampere, current density in A m^-2, drift velocity in m s^-1, resistance in ohm, resistivity in ohm metre, emf in volt, power in watt and energy in joule. The number density n comes in m^-3, so a value given per cm^3 must be multiplied by 10^6 before use.

Quantity	Expression	Note
Terminal voltage of a cell	emf minus I r	r is the internal resistance
Two cells in series	emfs add, resistances add	same current through both
Two cells in parallel	emf and r from the parallel formulas	used when currents divide
Wheatstone balance	P/Q = R/S	galvanometer carries no current
Potentiometer balance	emf proportional to balancing length	null method, no current drawn

Exam

In every circuit numerical write the two equations before substituting numbers: the junction equation and the loop equation. Then check the sign convention for each source and resistor. Sign errors are the usual cause of a wrong current direction.

in hinglish

Current electricity mein pehle microscopic picture samajh lo. Current charge ke flow ka rate hai, I = dQ/dt, aur current density J = n e v d hoti hai. Electron ka drift velocity bahut chhota hota hai, phir bhi current bada aata hai kyunki electrons ki sankhya bahut zyada hai. Ohm's law kehta hai V = I R, aur wire ka resistance rho l / A hota hai. Resistivity material ki property hai, resistance geometry ki. Temperature badhne par conductor ki resistivity badhti hai, semiconductor ki ghatti hai. Cell ka emf tab milta hai jab current nahi behta; current lete hi terminal voltage emf - I r ho jata hai. Kirchhoff ke do rules yaad rakho: junction par charge conserve hota hai aur loop mein energy conserve hoti hai. Wheatstone bridge balance par P/Q = R/S hota hai. Numericals mein units pehle badlo, current direction diagram par likho, aur sign convention ek baar fix karke hi chalo.