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Ohm's Law is the single most important equation in electronics and the one you will use more than any other in amateur radio. It describes the relationship between voltage, current, and resistance in an electrical circuit, and it forms the basis for nearly every calculation you will encounter — from sizing power supply wiring to understanding receiver sensitivity.
Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across those points and inversely proportional to the resistance:
V = I × R
Where:
This can be rearranged to solve for any of the three quantities:
I = V / R (to find current)
R = V / I (to find resistance)
A popular memory aid is the "Ohm's Law triangle." Draw a triangle with V at the top and I and R at the bottom corners. Cover the quantity you want to find: if you cover V, you see I × R; cover I, you see V over R; cover R, you see V over I.
By combining Ohm's Law with the basic power equation (P = V × I), you get a family of related formulas:
| To find | Formula | Alternative |
|---|---|---|
| Power | P = V × I | P = I² × R or P = V² / R |
| Voltage | V = I × R | V = P / I or V = √(P × R) |
| Current | I = V / R | I = P / V or I = √(P / R) |
| Resistance | R = V / I | R = P / I² or R = V² / P |
You do not need to memorise all twelve variations. If you know V = I × R and P = V × I, you can derive the rest.
Your HF transceiver draws 22 A on transmit and requires 13.8 V. Using P = V × I:
P = 13.8 × 22 = 303.6 W
You need a power supply rated for at least 304 W — in practice you would choose one with some margin, perhaps 350–400 W.
You are running a 3-metre cable from your power supply to your transceiver at 22 A. If the cable has a total resistance (both conductors) of 0.05 Ω, the voltage drop is:
V = I × R = 22 × 0.05 = 1.1 V
That means only 12.7 V arrives at the transceiver instead of 13.8 V — likely too low for reliable operation. You would need thicker wire (lower resistance) to keep the voltage drop under about 0.5 V.
A 470 Ω resistor has 9 V across it. The current flowing through it is:
I = V / R = 9 / 470 = 0.0191 A ≈ 19.1 mA
And the power dissipated by the resistor:
P = V × I = 9 × 0.0191 = 0.172 W
A quarter-watt (0.25 W) resistor would be sufficient, though using a half-watt resistor gives a comfortable safety margin.
In a series circuit, components are connected end-to-end so the same current flows through all of them. Key rules:
A common application of series resistors is the voltage divider — two resistors in series across a voltage source where you tap the voltage at the junction between them. The output voltage is:
V_out = V_in × R₂ / (R₁ + R₂)
Voltage dividers appear everywhere in radio circuits: biasing transistor stages, setting reference voltages, and creating signal attenuation.
In a parallel circuit, components are connected across the same two points so they share the same voltage. Key rules:
For the common case of just two resistors in parallel, there is a simpler formula:
R_total = (R₁ × R₂) / (R₁ + R₂)
The total resistance of a parallel combination is always less than the smallest individual resistor.
When you connect multiple speakers or dummy loads in parallel, the total impedance drops. Two 50 Ω dummy loads in parallel present 25 Ω to the transmitter — important to know before connecting them to equipment expecting a 50 Ω load.
Real circuits often combine series and parallel sections. To analyse them, simplify step by step: first combine parallel groups into their equivalent resistances, then add those in series (or vice versa) until you reduce the circuit to a single equivalent resistance. Apply Ohm's Law to the simplified circuit, then work backwards to find individual voltages and currents.
Ohm's Law applies to AC circuits as well, but resistance is replaced by impedance (Z), which accounts for both resistance and reactance:
V = I × Z
Impedance, reactance, and the behaviour of capacitors and inductors in AC circuits are covered on the AC Circuits page. The good news is that the structure of the calculations is identical — you are just working with more complex numbers.
For circuits that cannot be reduced to simple series-parallel combinations, Kirchhoff's Laws provide additional tools:
Kirchhoff's Current Law (KCL): The total current entering any junction equals the total current leaving it. This is a statement of conservation of charge.
Kirchhoff's Voltage Law (KVL): The sum of all voltages around any closed loop in a circuit is zero. This is a statement of conservation of energy.
These laws, combined with Ohm's Law, are sufficient to analyse any linear circuit. They are especially useful when working with multi-loop circuits found in amplifier designs and filter networks.
Electronics uses metric prefixes extensively. The ones you will encounter most often:
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| mega | M | × 1,000,000 | 3.5 MHz = 3,500,000 Hz |
| kilo | k | × 1,000 | 4.7 kΩ = 4,700 Ω |
| milli | m | × 0.001 | 50 mA = 0.050 A |
| micro | µ | × 0.000001 | 100 µV = 0.000100 V |
| nano | n | × 0.000000001 | 10 nF = 0.000000010 F |
| pico | p | × 0.000000000001 | 33 pF = 0.000000000033 F |
Being comfortable converting between these prefixes is essential for reading component values and working through calculations.
Ohm's Law and the related power formulas appear heavily on amateur radio licence exams worldwide. Practice these steps: