T5D: Ohm's Law and Circuits

Ohm's Law is the single most important relationship in basic electronics. It connects the three fundamental quantities — current, voltage, and resistance — in a simple set of formulas that allow you to calculate any one when you know the other two. Every circuit analysis problem in the Technician exam, and most real troubleshooting situations, comes back to Ohm's Law in one of its three forms.

T5D covers the three Ohm's Law formulas (for current, voltage, and resistance), applies each one through multiple calculation examples, and introduces the key properties that distinguish series circuits from parallel circuits.

Ohm's Law: Three Forms

Ohm's Law states that voltage equals current multiplied by resistance. From this single relationship, three equivalent formulas can be derived — one for each quantity you might need to find:

The variable names used in these formulas follow the traditional convention: E for electromotive force (voltage), I for intensity (current), and R for resistance. Some sources use V for voltage instead of E — both conventions appear in amateur radio materials, but the exam pool uses E.

The key to getting the right formula is knowing which quantity you are solving for. If the problem gives you voltage and resistance and asks for current, use I = E / R. If it gives current and resistance and asks for voltage, use E = I × R. If it gives voltage and current and asks for resistance, use R = E / I.

Calculating Resistance

Using R = E / I, you can find the resistance of any circuit when voltage and current are known. The T5D exam includes three resistance calculations:

All three are straightforward divisions. The common error is using the wrong formula — if you multiply instead of divide, you will get a result in watts (power) rather than ohms (resistance). Always divide voltage by current to find resistance.

Calculating Current

Using I = E / R, you can find current when voltage and resistance are known. The T5D exam includes three current calculations:

Each is a division of voltage by resistance. The result is in amperes. Notice that higher resistance for the same voltage produces lower current (120 V through 80 Ω = 1.5 A), and lower resistance produces more current (240 V through 24 Ω = 10 A) — this inverse relationship between current and resistance (for fixed voltage) is what Ohm's Law expresses.

Calculating Voltage

Using E = I × R, you can find the voltage across a resistor when current and resistance are known. The T5D exam includes three voltage calculations:

Each is a multiplication of current by resistance. The last two examples use the same 10-ohm resistor with different currents (1 A and 2 A), producing voltages of 10 V and 20 V respectively — doubling the current doubles the voltage across the same resistance, which is exactly what Ohm's Law predicts.

Series and Parallel Circuits

Components can be connected in two fundamental arrangements: series and parallel. Understanding which property is constant in each type is essential.

Series circuits connect components end-to-end in a single path. Current has only one route to flow, so the same current flows through every component in the series chain. Voltage, however, divides across the components — each one has a voltage drop proportional to its resistance. In a series circuit, DC current is the same through all components.

Parallel circuits connect components side by side, with both ends of each component connected to the same two nodes. Each component has the full supply voltage across it, so voltage is the same across all components. Current, however, divides — the total current splits among the parallel branches in inverse proportion to their resistances. In a parallel circuit, voltage is the same across all components.

This distinction is practically important in station wiring. Your transceiver and power supply are connected in series with the DC power leads — the same current flows through both the positive and negative wires. Your antenna, SWR meter, and feed line form a series RF circuit from transmitter to antenna. Multiple loads in a vehicle electrical system (lights, radio, etc.) are connected in parallel — each gets the same 12 V supply voltage regardless of the others.

T5D Practice Questions