05 Electric Current and Ohm’s Law

Electric current (I)

The rate at which electric charge passes through a cross-sectional area.

Electric current formula

I = ΔQ/Δt

Charge transferred

Q = IΔt

SI unit of current

Ampere (A); 1 A = 1 C/s.

Conventional current direction

The direction positive charges would move; opposite electron flow in a metal.

Current density (J)

Electric current per unit cross-sectional area.

Current density formula

J = I/A, for uniform current density.

SI unit of current density

A/m².

Drift velocity

Average velocity attained by charge carriers due to an electric field.

Current and drift velocity

I = nqAvd

Drift velocity formula

vd = I/(nqA), using magnitudes.

Charge carrier density (n)

Number of charge carriers per unit volume, measured in m⁻³.

Charge carrier charge (q)

Magnitude of charge per charge carrier, measured in coulombs.

Cross-sectional area (A)

Area perpendicular to current flow, measured in m².

Resistance (R)

A measure of opposition to the flow of electric charge.

Resistance formula

R = ρL/A

Resistivity (ρ)

A material property measuring opposition to electrical conduction.

SI unit of resistance

Ohm (Ω).

SI unit of resistivity

Ohm-meter (Ω·m).

Ohm's law

V = IR

Current from Ohm's law

I = V/R

Resistance from Ohm's law

R = V/I

Voltage from Ohm's law

V = IR

Non-ohmic material

A material whose current is not directly proportional to voltage.

Kirchhoff's junction rule

The total current entering a junction equals the total current leaving it.

Kirchhoff's loop rule

The algebraic sum of potential differences around a closed loop is zero.

Resistors in series

Req = R₁ + R₂ + …

Current through series resistors

The same current flows through every resistor.

Voltage across series resistors

The total voltage equals the sum of individual voltage drops.

Resistors in parallel

1/Req = 1/R₁ + 1/R₂ + …

Voltage across parallel resistors

The voltage across each resistor is the same.

Current through parallel resistors

The total current equals the sum of the branch currents.

Electric power (P)

The rate at which electrical energy is transferred or consumed.

Electric power formula

P = IV

Power using current and resistance

P = I²R

Power using voltage and resistance

P = V²/R

SI unit of power

Watt (W); 1 W = 1 J/s.

Electrical energy transferred

E = Pt, for constant power over time.

Charge of an electron

Approximately −1.602 × 10⁻¹⁹ C.

Elementary charge magnitude

e = 1.602 × 10⁻¹⁹ C.