Ohm's Law Explained: The Foundation of Every Circuit
V = IR in Plain English
Ohm's Law says that voltage equals current times resistance: V = I x R. Rearranged, it also gives us I = V/R and R = V/I. These three forms answer every basic circuit question. Think of it like water in a pipe. Voltage is the water pressure, current is the flow rate (how much water moves per second), and resistance is the pipe's narrowness. Higher pressure pushes more water through a given pipe. A narrower pipe restricts flow for any given pressure. The analogy is not perfect, but it gets the intuition right. Voltage is measured in volts (V), current in amps (A), and resistance in ohms (the Greek letter omega). A standard AA battery provides 1.5V. A USB port supplies 5V at up to 0.5A (USB 2.0) or 3A (USB-C PD). A household outlet in the US delivers 120V at up to 15A or 20A. When you plug a 100-ohm resistor across a 5V supply, the current is I = 5/100 = 0.05A, or 50 milliamps. That single calculation is the foundation of sizing every resistor in every circuit. Try it yourself with the <a href="/electronics/ohms-law">Ohm's Law Calculator</a>.
Practical Examples You Will Actually Use
Here are four real scenarios where Ohm's Law solves the problem. LED current limiting: You have a red LED (2V forward voltage, 20mA rated current) and a 9V battery. The resistor needs to drop the remaining 7V (9V - 2V) at 20mA. R = V/I = 7/0.020 = 350 ohms. The nearest standard value is 360 ohms, which gives 19.4mA. Safe and bright. Our <a href="/electronics/led-resistor">LED Resistor Calculator</a> does this instantly for any LED and supply voltage. Speaker impedance: Your amplifier outputs 12V and your speaker is rated at 8 ohms. The current drawn is I = 12/8 = 1.5A. The power dissipated in the speaker is P = V x I = 18 watts. If your speaker is only rated for 15W, you will damage it. Voltage dividers: Two resistors in series split a voltage proportionally to their resistance values. A 10K and 20K resistor across 12V create an output of 12 x (20K / (10K + 20K)) = 8V at the junction. The <a href="/electronics/voltage-divider">Voltage Divider Calculator</a> handles this. Fuse sizing: A 120V appliance draws 8A. If you need a fuse, you want one rated just above 8A, so a 10A fuse. The appliance resistance is R = 120/8 = 15 ohms. If the resistance drops (short circuit), current spikes and the fuse blows.
Power: The Fourth Variable
Power is not part of Ohm's Law directly, but it is inseparable in practice. Power (in watts) equals voltage times current: P = V x I. Combining with Ohm's Law gives us P = I squared x R and P = V squared / R. These power equations determine how hot a resistor gets and therefore what size (wattage rating) you need. That 350-ohm LED resistor carrying 20mA dissipates P = (0.020)^2 x 350 = 0.14 watts. A standard 1/4-watt resistor handles this easily. But a 10-ohm resistor carrying 1A dissipates P = 1^2 x 10 = 10 watts and needs a large, heatsunk power resistor. This is why short circuits are dangerous. If a wire shorts across a 12V car battery with only 0.01 ohms of resistance, the current is I = 12/0.01 = 1,200A. The power is P = 12 x 1200 = 14,400 watts. That instantly melts wire insulation and can start fires, which is exactly why fuses and circuit breakers exist. When sizing components, always calculate the power dissipation and choose parts rated for at least double the calculated value. A resistor dissipating 0.3W should be rated for at least 0.5W, preferably 1W. Derating extends component life significantly.
Common Mistakes and Misconceptions
The most frequent error is mixing units. Ohm's Law requires volts, amps, and ohms. If you work in milliamps, you must either convert to amps (divide by 1000) or express resistance in kilohms to cancel out. 5V across 2.2K ohms = 5/2200 = 0.00227A = 2.27mA. Alternatively, 5V / 2.2K = 2.27mA if you keep milliamps and kilohms consistent. Another common mistake is applying Ohm's Law to non-linear components. LEDs, diodes, and transistors do not obey Ohm's Law because their resistance changes with applied voltage. An LED does not have a fixed resistance. Instead, it has a forward voltage (roughly constant) and the current is set by the external resistor. That is why we subtract the LED's forward voltage before calculating. People also confuse series and parallel resistance. Two 100-ohm resistors in series give 200 ohms. In parallel, they give 50 ohms (1/(1/100 + 1/100) = 50). This matters because accidentally wiring a speaker in parallel with another halves the total impedance and doubles the current draw from the amplifier. Finally, Ohm's Law applies to DC circuits and to AC circuits at a single frequency only when you account for impedance (resistance + reactance), not just resistance.
From Ohm to Kirchhoff: What Comes Next
Ohm's Law handles single components. Real circuits have multiple branches, and that is where Kirchhoff's laws take over. Kirchhoff's Voltage Law (KVL) says that the sum of all voltages around any closed loop in a circuit equals zero. If you have a 9V battery and three resistors dropping 3V, 4V, and 2V, the loop checks out: 9 - 3 - 4 - 2 = 0. If it does not add up, you measured something wrong. Kirchhoff's Current Law (KCL) says that all current entering a node equals all current leaving it. If 50mA flows into a junction and splits into two branches, the branch currents must add to 50mA. In practice, you use Ohm's Law to calculate voltage drops and currents in individual components, then use Kirchhoff's laws to verify that the whole circuit is consistent. This combination handles everything from simple LED circuits to complex amplifier designs. For everyday electronics work like Arduino projects, LED strips, and sensor circuits, Ohm's Law plus basic series and parallel resistance is enough. The <a href="/electronics/ohms-law">Ohm's Law Calculator</a> handles the arithmetic so you can focus on the design decisions.
Try These Calculators
Put what you read into practice with these free calculators.