While static electricity explores charges at rest, current electricity is all about charges in motion. This continuous flow of electric charge is what powers the vast majority of our modern world, from the lights in our homes to the sophisticated electronics we use daily.

Electric current (I) is formally defined as the net rate of flow of electric charge past a specific point or through a cross-section of a conductor over a given period of time.

I = tQ
Where:
● I represents the electric current, measured in Amperes (A).
● Q represents the quantity of electric charge, measured in Coulombs (C).
● t represents the time taken for the charge to flow, measured in seconds (s).
Therefore, one Ampere is defined as one Coulomb of charge flowing past a point every second (1 A = 1 C/s).

When electricity was first studied, it was assumed that positive charges moved from the positive terminal of a battery to the negative terminal. This direction is still used today and is called conventional current. However, we now know that in most common conductors (like metals), it is the negatively charged electrons that actually move, flowing from the negative terminal to the positive terminal.

For charges to flow and create a current, there must be an energy difference between two points in a circuit, providing the "push" or "drive" for the charges. This energy difference is known as voltage or potential difference. Potential difference (V) between two points is defined as the work done (or energy transferred) per unit positive charge as that charge moves from one point to the other.

V = QW (where W is work done or energy transferred)
Where:
● V represents the potential difference (voltage), measured in Volts (V).
● W (or E for energy) represents the work done or energy transferred, measured in Joules (J).
● Q represents the quantity of electric charge, measured in Coulombs (C).

As electric charges move through a material, they collide with the atoms and ions within the material. These collisions impede the free flow of charge, resulting in resistance. Resistance is the property of a material that opposes the flow of electric current through it.

The crucial relationship between voltage, current, and resistance in a circuit was discovered by Georg Simon Ohm and is known as Ohm's Law. It states that for a given metallic conductor at a constant temperature, the current flowing through it is directly proportional to the potential difference across its ends.

Expressed as a formula:
V = I × R
Where:
● V is the voltage (potential difference) across the component, in Volts (V).
● I is the current flowing through the component, in Amperes (A).
● R is the resistance of the component, measured in Ohms (Ω).

The resistance of a wire or conductor is not a fixed value for all conductors; it depends on several factors:
1. Length (L): The longer the wire, the more opportunities there are for electrons to collide with atoms, thus increasing resistance. Resistance is directly proportional to length.
2. Cross-sectional Area (A): A thicker wire (larger cross-sectional area) provides more space for electrons to flow through, reducing the number of collisions. Resistance is inversely proportional to cross-sectional area.
3. Material (Resistivity, ρ): Different materials have different inherent abilities to conduct electricity. Some materials (like copper) naturally offer very little resistance (low resistivity), making them good conductors. Others (like rubber) offer very high resistance (high resistivity), making them good insulators.
4. Temperature (T): For most metallic conductors, increasing the temperature causes the atoms within the material to vibrate more vigorously. This increased vibration makes it more difficult for electrons to pass through, leading to an increase in resistance.

In series circuits, components are connected end-to-end, forming a single, continuous path for the electric current. The current must pass through each component sequentially.
● Current (I): The current is the same at every point in a series circuit.
● Voltage (V): The total voltage provided by the power source is divided among the components.
● Resistance (R): The total equivalent resistance of a series circuit is the sum of the individual resistances of all the components.

In parallel circuits, components are connected across each other, creating multiple independent paths for the current to flow. Each component is directly connected to the full voltage of the power source.
● Current (I): The total current flowing from the power source is divided among the parallel branches.
● Voltage (V): The voltage is the same across every component connected in parallel.
● Resistance (R): The total equivalent resistance of a parallel circuit is always less than the resistance of the smallest individual resistor in the circuit.

Electrical power measures the rate at which electrical energy is converted into other forms of energy (e.g., light in a bulb, heat in a heater, motion in a motor). The general definition of power is the rate of doing work or energy transfer (P = W/t or P = E/t).

For electrical circuits, we can derive specific formulas using voltage and current:
Primary Electrical Power Formula:
P = V × I
Where:
● P is electrical power, in Watts (W).
● V is the voltage (potential difference) across the component, in Volts (V).
● I is the current flowing through the component, in Amperes (A).

Electricity, while incredibly useful, can be dangerous. Household electrical systems incorporate several critical safety features to minimize risks, including fuses, circuit breakers, and earthing (grounding).