A Beginner's Guide to Ohm's Law, Resistance, and Resistors

Ohm's law states that the current in a conductor or a closed circuit is proportional to the voltage across it and inversely proportional to the resistance of the conductor.

Because of Ohm's law, we have luxuries like room heaters, hair dryers, and incandescent light bulbs that work safely and predictably. Even though Georg Ohm discovered and formulated Ohm's law back in 1827, it is still widely used today in electrical engineering.

What Ohm's Law Means Physically

Memorizing equations can be stressful, and it's not the way to truly learn and understand science. Let's break down Ohm's law into its parts and try to grasp its meaning in real life.

Voltage Pushes, Resistance Restrains

To understand voltage, current, and resistance, imagine a tub of water.

If you move your hand through the water, the water flows in the direction you push it. The harder you push your hand, the more water moves. If you push more slowly or gently, less water flows.

As you move your hand deeper into the water, it becomes harder to move. The water resists your motion, making it harder to push the water around.

If we apply this metaphor to electricity,

• Voltage is how hard you push. In a circuit, voltage provides the energy that pushes electric charge through a conductor.
• Current is the amount of water flowing per second. In a circuit, it represents how much electric charge flows past a point each second.
• Resistance is the water pushing back against your hand. Higher resistance makes it harder for charge to flow, reducing the current.

Ohm's Law Equation and Explanation

$V = IR$

Each variable in Ohm's has a unit that tells you what it measures:

• V is voltage (Volts, $V$) measures the energy that drives electric charge through a conductor.
• I is current (Amperes, $A$) measures the rate at which electric charge flows past a point per second.
• R is resistance (Ohms, $\Omega$) Measures how much a material opposes the flow of current.

Ohm's law is also commonly rearranged as $R = \frac{V}{I}$ and $I = \frac{V}{R}$.

If you want to double check your answers, you can always use the interactive Ohm's Law calculator

Multiple Power Sources Connected in Series or Parallel

If you have multiple power sources connected in series, their voltages add up, like so:

$V_{total} = V_1 + V_2 + V_3 + ... + V_n$

You can think of this intuitively by remembering what voltage is in our metaphor: a push. If you stack all these pushes up, you get more of a push, but the same amount of flow (current).

If you have multiple power sources (of the same voltage) connected in parallel, their currents add up and voltage remains the same:

$I_{total} = I_1 + I_2 + I_3 + ... + I_n$

Think of this like pushing with both hands at once. Same amount of push, but you're getting more flow, or current.

Power sources connected in parallel must have the same voltage. If their voltages differ, large currents can flow between the sources, potentially causing overheating or damage.

Resistors and How They Apply to Ohm's Law

Resistors, like their name implies, add resistance to a circuit. To calculate the resistance they add to a circuit, you must first determine how they are connected.

Resistors in Series

$R_{total} = R_1 + R_2 + R_3 + ... + R_n$

To find the total resistance of resistors connected in series, add up all the resistors' values.

Resistors in Parallel

$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}$

Parallel is similar to series, but you take the inverse of the sum of all the resistors' values.

Resistors are commonly used to protect components like LEDs by resisting too much current to flow to the component.

Ohm's Law Practice Problems

You've learned about Ohm's law, now it's time to apply it in real circuits.

Beginner Level Problem

$5V$ is applied to a circuit that has a resistance of $100\Omega$. What is the resulting current?

Intermediate Problem

A circuit has a $12V$ battery connected to it and two resistors in series: $R_1 = 100\Omega$ and $R_2 = 200\Omega$.

• Find the total resistance.
• Find the current flowing through the circuit.
• Find the voltage drop across each resistor.

Harder Problem

A power source of $9V$ and a maximum current output of $500mA$ is connected in series with another power source of $12V$ and a maximum current output of $1A$. When placed on a circuit with a resistance of $360\Omega$, will the current exceed the maximum output of the $9V$ power source?

What is Ohm's Law is Used for in Real Life

As demonstrated in the practice problems, Ohm's law isn't just an equation. It is a useful tool used to design, test, and repair electrical systems.

Engineers and technicians use Ohm's law for

• Selecting safe power supplies so components are not overdriven
• Limiting current to sensitive parts like LEDs, microcontrollers, and sensors
• Predicting heat generation in wires, resistors, and heating elements
• Diagnosing faults, such as short circuits or open connections

In the video below, Ohm's law is applied directly using a variable power supply and a nichrome wire:

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As you can see on the power supply's display, as the voltage increases, the current increases as well, making the wire glow red-hot.

This is a visible demonstration of Ohm's law in action:

• Voltage increases
• Resistance stays (roughly) the same
• Current must increase

Another equation plays into this as well, called the Power law (or Joule's law), which explains why increased current leads to rapid heating.

Conclusion

Ohm's law defines the fundamental relationship between voltage, current, and resistance, making it one of the most important laws in all of electronics and electrical engineering.

Rather than being just a formula to memorize, Ohm's law explains why circuits behave the way they do. It tells you what will happen before you apply power; whether a component will operate safely, overheat, or fail.

By understanding voltage as a push, current as flow, and resistance as opposition, you gain the ability to reason through circuits instead of guessing. This conceptual understanding is what separates beginners from confident problem-solvers.

Once Ohm's law is mastered, more advanced topics like power dissipation, circuit analysis, and digital electronics become far easier to understand. It is not an exaggeration to say that nearly every electrical system rests on this single relationship. Check out the article on other fundamental laws of circuits to learn more.