Electricity and Magnetism - Electrical quantities (Current, voltage and resistance)

Electric Current ($I$) is the rate of flow of electric charge ($Q$). It is measured in Amperes ($A$) using an ammeter connected in series. Charge is measured in Coulombs ($C$).

Conventional current flows from the positive terminal to the negative terminal, whereas electrons (the actual charge carriers in metals) flow from negative to positive.

Potential Difference ($V$), often called voltage, is the work done per unit charge in moving a charge between two points. It is measured in Volts ($V$) using a voltmeter connected in parallel.

Electromotive Force (e.m.f.) is the energy supplied by a source (like a battery) in driving unit charge around a complete circuit. Its unit is also the Volt ($V$).

Resistance ($R$) is the property of a component that opposes the flow of electric current. It is defined as the ratio of potential difference to current ($R = \frac{V}{I}$) and measured in Ohms ($\Omega$).

Ohm's Law states that the current through a conductor is directly proportional to the potential difference across it, provided physical conditions like temperature remain constant ($V ∝ I$).

The resistance of a wire is directly proportional to its length ($L$) and inversely proportional to its cross-sectional area ($A$), given by the relationship $R \propto \frac{L}{A}$.

In a series circuit, the total resistance is the sum of individual resistances: $R_{total} = R_1 + R_2 + ...$. The current is the same at all points.

In a parallel circuit, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances: $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$. The voltage across each branch is the same.