Ohm's Law
Ohm's Law is the single most important equation in all of electronics. It describes the relationship between three quantities you already know from the previous lessons — voltage, current and resistance — and it lets you calculate any one of them when you know the other two. Every circuit calculation in this course builds on it, and you will use it constantly as a radio operator.
The Water Pipe Analogy
Before we touch a single formula, here is an everyday picture that makes Ohm's Law obvious.
Imagine a water tank raised up on a stand, connected to a pipe at the bottom. The water in the tank is under pressure because of gravity. Water flows out of the pipe, through a tap, and away. That system has three things you can adjust:
- The height of the tank — the higher the tank, the more water pressure there is pushing down. This is voltage.
- How fast the water flows — measured in liters per minute. This is current.
- How narrow the pipe is — a thin pipe restricts the flow. A wider pipe lets more through. This narrowing is resistance.
Here is the key insight: if you increase the pressure (raise the tank), more water flows — current goes up. If you narrow the pipe (increase resistance), less water flows for the same pressure — current goes down. These three quantities are linked. You cannot change one without affecting the others.
Voltage is the pressure pushing current through the circuit, just like a pump pushes water through a pipe. Resistance narrows the pipe and reduces the flow.
View LargerOhm's Law puts a precise number on that relationship. It tells you exactly how much current flows when a given voltage pushes against a given resistance.
Voltage, Current and Resistance — A Quick Recap
You covered these in detail in the previous three lessons. Here is a short reminder of what each symbol means:
| Symbol | Quantity | Unit | What it means |
|---|---|---|---|
| V | Voltage | Volts (V) | The electrical pressure pushing current around the circuit |
| I | Current | Amperes / amps (A) | The rate of flow of electric charge |
| R | Resistance | Ohms (Ω) | How strongly a component opposes current flow |
The unit of resistance is named after Georg Ohm, the German physicist who discovered the relationship we are about to look at.
What Ohm's Law States
Ohm's Law says: the current flowing through a conductor is directly proportional to the voltage across it, and inversely proportional to its resistance.
In plain English: double the voltage and you double the current. Double the resistance and the current halves. Written as a formula:
That is it. One formula. Three letters. Everything else in this lesson is just using that formula in different ways.
The Formula Triangle
A simple trick helps you remember which version of the formula to use. Draw a triangle and divide it into three sections: V on top, I and R side by side on the bottom.
The Ohm's Law triangle. Cover the quantity you want to find and the remaining two symbols show the operation: side by side means multiply, one above the other means divide.
View LargerTo use the triangle:
- Cover V — you see I × R. So V = I × R.
- Cover I — you see V above R. So I = V ÷ R.
- Cover R — you see V above I. So R = V ÷ I.
The triangle is a memory aid, not a magic formula. Understanding why the three forms work is more useful than memorising the triangle, so let us look at each form in detail.
The Three Forms of Ohm's Law
Form 1 — V = I × R (Finding Voltage)
Use this when you know the current and the resistance and want to find the voltage.
Practical meaning: if you push 2 amps through a 10 Ω resistor, the voltage across that resistor will be 20 V. The resistor is dropping (using up) 20 volts of the supply.
V = I × R = 0.1 × 47 = 4.7 V
Form 2 — I = V ÷ R (Finding Current)
Use this when you know the voltage and the resistance and want to find how much current flows.
Practical meaning: if you connect a 100 Ω resistor across a 12 V supply, 120 mA of current flows. This is the most frequently used form in practice — you almost always know your supply voltage and the load resistance.
I = V ÷ R = 12 ÷ 470 = 0.0255 A (25.5 mA)
Form 3 — R = V ÷ I (Finding Resistance)
Use this when you know the voltage and the current and want to find the resistance — or when you want to calculate what resistance value you need to achieve a target current.
Practical meaning: if your supply is 12 V and you want no more than 50 mA to flow through a component, you need at least 240 Ω of resistance in the circuit.
R = V ÷ I = 12 ÷ 0.5 = 24 Ω
Those are the only three operations. The calculator below handles all of them automatically — just enter any two values and leave the third blank.
Ohm's Law Calculator
Ohm's Law Solver — V, I and R
Enter any two values and leave the third blank. The calculator will solve for the missing quantity. Use decimal notation (e.g. 0.025 for 25 mA).
Leave exactly one field empty — that is the value to be calculated.
Ham Radio Worked Examples
Let us put Ohm's Law to work on real problems you will encounter in a ham shack.
Example 1 — Resistor for a 5 V Fan on a 12 V Supply
You are building a small enclosure for a homebrew VHF kit. The 5 V cooling fan you have rated draws 200 mA (0.2 A), but your supply rail is 12 V. You need a series resistor to drop the extra voltage.
The resistor needs to drop: 12 V − 5 V = 7 V, while carrying 0.2 A.
The nearest standard values are 33 Ω (slightly faster fan) or 39 Ω (slightly slower). Either works. Choose 33 Ω for better cooling.
You should also check how much power the resistor will dissipate — we cover that in the Power section below, but the answer is 1.4 W, so use a 2 W rated resistor.
Example 2 — Fuse Sizing for an HF Transceiver
Your new 100 W HF transceiver runs from a 13.8 V supply. You need to choose the correct fuse for the power cable. The transceiver draws its highest current during transmit.
A 100 W radio at 50% efficiency (typical for class AB) draws about 200 W from the supply at full power. How much current is that?
Select the next standard fuse size above that: a 20 A fuse. Never use a fuse below the calculated current, or it will blow during normal transmit.
Note: here we used P = V × I rearranged to I = P ÷ V. This is a power formula but it uses voltage from Ohm's Law — the two go hand in hand.
Example 3 — Voltage Drop on a Long Power Cable
Your power supply is 4 metres away from your radio. The 12 AWG cable you are using has a resistance of about 5.2 mΩ per metre (0.0052 Ω/m). The total cable run is 8 m (4 m there and 4 m back along the return conductor).
Total cable resistance = 8 × 0.0052 = 0.0416 Ω
During a 10 A transmit burst, how much voltage is lost in the cable?
Your 13.8 V supply arrives at the radio as 13.38 V — acceptable.
Now try 20 A (a higher-power radio): V = 20 × 0.0416 = 0.83 V
Radio sees only 12.97 V. Getting close to the lower operating limit. Use heavier cable.
This is why the ARRL and most manufacturers recommend keeping the run between power supply and radio as short as possible, with heavy-gauge wire.
Power and Ohm's Law
Ohm's Law tells you about V, I and R. When you add power (P, measured in watts) to the picture, you get three more useful relationships:
P = I² × R — Power equals current squared times resistance
P = V² ÷ R — Power equals voltage squared divided by resistance
These are derived by combining P = V × I with V = I × R. You do not need to memorise all three separately — they all come from the same two equations. In practice, you use whichever form has the two quantities you already know.
The power formula wheel. Each segment shows how to find one of the four quantities (P, V, I, R) from any other two. All twelve expressions come from combining Ohm's Law with P = VI.
View LargerWhy does this matter for ham radio? Power is what causes components to heat up. The resistor in Example 1 above dissipates P = I² × R = 0.2² × 35 = 1.4 W. A 0.25 W resistor would burn out. The power calculator below handles all these combinations automatically.
Power Formula Calculator
Power, Voltage, Current and Resistance Calculator
Enter any two of the four values below and leave the other two blank. All remaining quantities will be calculated from P = VI, P = I²R and P = V²/R.
Leave exactly two fields empty — those are the values to be calculated.
Summary
| You want to find | Formula | You need to know |
|---|---|---|
| Voltage (V) | V = I × R | Current and Resistance |
| Current (I) | I = V ÷ R | Voltage and Resistance |
| Resistance (R) | R = V ÷ I | Voltage and Current |
| Power (P) | P = V × I | Voltage and Current |
| Power (P) | P = I² × R | Current and Resistance |
| Power (P) | P = V² ÷ R | Voltage and Resistance |
Frequently Asked Questions
Does Ohm's Law work for AC circuits?
Yes and no. For a purely resistive load (a heater element, a dummy load, a resistor) Ohm's Law works exactly the same way in AC as in DC — V = I × R holds, and you use the RMS values of voltage and current. However, when capacitors or inductors are in the circuit, they oppose current in a frequency-dependent way called reactance. The generalised version of Ohm's Law for AC uses impedance (Z) in place of resistance: V = I × Z. Impedance includes both resistance and reactance. You will cover this in Module 6 (AC Circuit Theory). For now, work with the resistive version of the law — it is correct for all DC circuits and for the resistive portions of AC circuits.
What happens if resistance is zero?
If resistance is truly zero, the formula I = V ÷ R means dividing by zero, which is mathematically undefined. In the real world it means the current is theoretically unlimited — any voltage, no matter how small, would drive an infinite current. This is a short circuit. In practice, the wire, the battery's internal resistance and the connection itself always add a tiny amount of resistance, so the current is very large but not truly infinite. It is large enough to blow fuses, melt wire insulation and cause fires, which is why short circuits are dangerous. Superconductors are a special case where resistance really does reach zero at very low temperatures, and they are used in MRI machines and particle accelerators where the property is deliberately exploited.
Why does my calculated answer seem wrong? (Unit mismatch)
The most common cause of a surprising answer is a unit mismatch. Ohm's Law requires all values in base units: volts, amperes and ohms. If your current is in milliamps, you must convert it to amps before using the formula. 250 mA is 0.25 A. If your resistance is in kilohms, convert it: 4.7 kΩ is 4700 Ω. A typical mistake: R = 12 ÷ 250 gives 0.048, not 48 Ω, because 250 was in milliamps, not amps. The correct calculation is R = 12 ÷ 0.250 = 48 Ω. Always check your units first.
Is Ohm's Law always exact, or are there limitations?
Ohm's Law is exact for ohmic (linear) materials — most metals, carbon-composition resistors and wire-wound resistors. However, some components are deliberately non-ohmic: diodes, transistors and LEDs have a non-linear voltage-to-current relationship, so a simple V = IR calculation will not predict their behavior accurately. Temperature also matters — a resistor's value drifts slightly with temperature, and a light bulb filament has much higher resistance when hot than when cold. For circuits containing only resistors operating within their temperature limits, Ohm's Law is precise. For diodes, transistors and RF components, you need more advanced models, which you will encounter later in this course.
Why is current called I instead of C?
The symbol I comes from the French intensité du courant (intensity of current), used by early French physicists who formalised much of electrical theory. The letter C was already in use for capacitance and charge, so engineers kept I for current to avoid confusion. You will also see the symbol A used for the unit (ampere), but the variable itself is always I in circuit equations.
Test Your Knowledge
Answer the questions below to check your understanding of this lesson. Every answer can be found in the lesson above.