Fundamentals of Electricity: Voltage, Current, Resistance, and Power

Exam Tip: Always distinguish between "Potential" (Voltage) and "Flow" (Current). A battery sitting on a table has voltage, but it has zero current until it is connected to a load.

Resistance (R): The Obstacle to Flow

Resistance, measured in Ohms ($\Omega$), is the property of a material that opposes the flow of electric current. Every component in a circuit—from a copper wire to a lightbulb filament—offers some degree of resistance.

High resistance makes it harder for current to pass, while low resistance allows current to flow more easily. For example, a thin wire has higher resistance than a thick wire of the same material, which is why wire gauge is a critical factor in electrical safety and efficiency.

Ohm's Law: The Mathematical Connection

The relationship between Voltage, Current, and Resistance is defined by Ohm's Law. This law is the most important formula in basic electronics, stating that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance.

The primary formula is:

$$I = \frac{V}{R}$$

From this base equation, we can derive the others to solve for any missing variable:

$$\begin{aligned} V &= I \cdot R \\ R &= \frac{V}{I} \end{aligned}$$

Worked Example: Calculating Current

Imagine you have a 120V outlet in your home and you plug in a heater that has a resistance of 15 $\Omega$. To find the current flowing through the heater, you apply Ohm's Law:

$$\begin{aligned} I &= \frac{120\text{V}}{15\Omega} \\ I &= 8\text{A} \end{aligned}$$

The heater will draw 8 Amps of current.

Power (P): The Rate of Energy Transfer

While Voltage, Current, and Resistance describe the "how" of electricity, Power describes the "work" being done. Power, measured in Watts (W), is the rate at which electrical energy is consumed or converted into another form of energy, such as heat, light, or motion.

The fundamental formula for power is:

$$P = V \cdot I$$

By combining the Power formula with Ohm's Law, we can calculate power using only two of the other three variables. This is incredibly useful in real-world scenarios where you might know the voltage and the resistance but not the current.

$$\begin{aligned} P &= V \cdot I \\ P &= I^2 \cdot R \\ P &= \frac{V^2}{R} \end{aligned}$$

Worked Example: Calculating Power

Using the same heater from our previous example (120V and 8A), let's find out how much power it consumes:

$$\begin{aligned} P &= 120\text{V} \cdot 8\text{A} \\ P &= 960\text{W} \end{aligned}$$

The heater consumes 960 Watts of power.

Summary Table of Relationships

To help consolidate these concepts, refer to the following table:

Understanding these four pillars allows you to predict how a circuit will behave, ensuring that components are sized correctly and that electrical systems operate safely and efficiently.