If there is one equation every electrical engineer and hobbyist memorizes, it is Ohm’s law: V equals IR. Voltage equals current times resistance. Simple as it looks, this relationship underpins virtually every circuit ever built. Understanding it properly is the first step to working with electronics, whether you are wiring a house, designing a circuit board, or just replacing a blown fuse.
Voltage, measured in volts, is the electrical push that drives current through a circuit. Think of it like water pressure in a pipe. Higher voltage means more push. Current, measured in amps, is the flow of electrons through the wire. It is analogous to the volume of water flowing. Resistance, measured in ohms, is anything that opposes the current. A narrow pipe has more resistance than a wide one. A long thin wire has more resistance than a short thick one.
A simple example: a 12-volt battery connected to a 6-ohm resistor pushes 2 amps of current through it. Increase the resistance to 12 ohms, and the current drops to 1 amp. Increase the voltage to 24 volts with the original 6-ohm resistor, and the current doubles to 4 amps. These relationships are linear, which makes calculations straightforward. Try it with our Ohm’s Law Calculator.
Power is closely related. Electrical power equals voltage times current, or P equals VI. Using Ohm’s law, you can also write this as I squared R or V squared over R. A space heater drawing 10 amps from a 120-volt outlet consumes 1,200 watts. That same heater on a 240-volt European outlet at 5 amps also consumes 1,200 watts. The power is the same, but the voltage and current trade off.
Resistors are the most basic electronic component. They come in standard values and are marked with color bands. A brown-black-red-gold resistor is 1,000 ohms with 5% tolerance. Our Resistor Color Code Calculator helps decode these quickly. In circuit design, resistors limit current, divide voltages, and set timing in RC circuits.
Kirchhoff’s laws extend Ohm’s law to more complex circuits. The current law states that current entering a junction equals current leaving it. The voltage law states that the sum of voltages around any closed loop is zero. Combined with Ohm’s law, you can analyze any circuit, no matter how complex.
Real-world conductors have resistance too. Copper wire has a resistivity of about 1.68 micro-ohm-centimeters. A 100-meter run of 2.5 mm² copper wire has a resistance of roughly 0.68 ohms. For high-current applications like welders or EV chargers, this resistance causes voltage drop and heat generation, which is why thicker wire is used.
Safety is paramount when working with electricity. Ohm’s law tells us that even low voltages can be dangerous if the resistance is low enough. Wet skin has a resistance of only about 1,000 ohms, meaning 120 volts can push 120 milliamps through your body. That is enough to cause cardiac arrest. Always use insulated tools, turn off power before working, and respect the math.