Charge, Current, and Voltage

Electricity powers the modern world, but at its core, it is simply the movement and interaction of subatomic particles. To understand electrical engineering, we must first understand the three most fundamental quantities: charge, current, and voltage.

Electric Charge ($q$)

Electric charge is a fundamental physical property of matter. Protons have a positive charge, electrons have a negative charge, and neutrons have no charge. In most electrical circuits, the moving charges are electrons.

The unit of charge is the Coulomb (C). One Coulomb is an immense amount of charge — it represents the charge of approximately $6.242 \times 10^{18}$ electrons.

In formulas, charge is represented by the variable $q$ (or $Q$ for constant charge).

Electrical Current ($I$)

While charge is the fundamental property, electrical current is the rate of flow of that charge over time. If you imagine a wire as a pipe, current is the flow rate of the water moving through it.

Current is defined mathematically as the derivative of charge with respect to time:

$I = \frac{dq}{dt}$

where:

• $I$ = current in Amperes [A]
• $q$ = charge in Coulombs [C]
• $t$ = time in seconds [s]

One Ampere (A) is defined as the flow of one Coulomb of charge per second (1 A = 1 C/s).

Engineering Note: By historical convention, we use "conventional current," which flows from positive to negative. We maintain this convention in engineering analysis even though the physical electrons actually move from negative to positive.

Voltage (Potential Difference) ($V$)

Current tells us that charge is moving, but why does it move? It moves because energy is expended to push it.

Voltage, also known as electric potential difference, is the energy required to move a unit charge between two specific points. If current is the flow rate of water, voltage is the pressure pushing the water.

$V = \frac{W}{q}$

where:

• $V$ = voltage in Volts [V]
• $W$ = energy or work in Joules [J]
• $q$ = charge in Coulombs [C]

One Volt (V) is defined as one Joule of energy per Coulomb of charge (1 V = 1 J/C).

Whenever we specify a voltage, it is always a relative measurement between two points (a potential difference). A "12V battery" means there is a 12-volt potential difference between its positive and negative terminals.

Summary of Relationships

• Charge ($q$) is the fundamental "stuff" that experiences electrical forces.
• Current ($I$) is how fast that charge is moving.
• Voltage ($V$) is the energy push driving the charge to move.

Understanding these three quantities is the required prerequisite for understanding resistance and Ohm's Law, which tie them all together in practical circuits.