Ohm’s Law Applied
Part of Electrical Theory
Taking V=IR from a formula to a practical tool for sizing wire, choosing resistors, designing circuits, and diagnosing faults.
Why This Matters
Ohm’s Law is the most used equation in electrical work. Every wire size decision, every fuse rating, every generator design, every troubleshooting procedure relies on the relationship V = I × R. But the law is often taught as an abstraction to be memorized, when its real value is in application.
This article is about using Ohm’s law in the real world — with real materials, real uncertainties, and real consequences. A small wire on an overloaded circuit doesn’t just fail an exam question, it starts a fire. Getting the calculations right matters.
The Three Forms
Ohm’s Law (V = IR) rearranges into three forms, each useful in different situations:
V = I × R — find voltage from current and resistance (voltage drop in a wire, voltage across a load)
I = V / R — find current from voltage and resistance (how much current a circuit will draw, size the fuse)
R = V / I — find resistance from voltage and current (measure resistance with ammeter and voltmeter, identify resistance of unknown component)
Also derived: P = V × I = I² × R = V² / R (power, needed for calculating heat in resistors, wire ratings, fuse sizing)
Practical Application 1: Wire Sizing
The most common application — will this wire handle the current without overheating?
Given: 230V supply, 1500W heater, 15-meter run.
Step 1: Find current. I = P / V = 1500 / 230 = 6.5A
Step 2: Determine acceptable voltage drop. Typically 3–5% for most circuits; 2% for sensitive loads. V_drop_max = 230 × 0.03 = 6.9V (using 3%)
Step 3: Maximum acceptable wire resistance (total, both ways = 30m). R_max = V_drop / I = 6.9 / 6.5 = 1.06Ω
Step 4: Maximum resistance per meter. r_max = 1.06 / 30 = 0.035 Ω/m
Step 5: Find wire with resistivity at or below this value.
| Wire size (copper) | Resistance (Ω/m) |
|---|---|
| 1.0 mm² | 0.0183 |
| 1.5 mm² | 0.0121 |
| 2.5 mm² | 0.00732 |
| 4.0 mm² | 0.00457 |
1.5mm² (0.0121 Ω/m) is below 0.035 Ω/m — adequate. Also check current capacity: 1.5mm² handles ~13A — adequate for 6.5A.
Practical Application 2: Fuse Sizing
Fuses protect wire from overcurrent. Size fuses to protect the wire, not the device.
Given: 2.5mm² copper wire, what is the appropriate fuse?
Current capacity of 2.5mm² copper wire (in conduit): approximately 16–20A depending on installation method and ambient temperature.
Fuse rating should be at or below 16A. Standard sizes: 10A, 13A, 16A. Choose 16A — it protects the wire while allowing the circuit’s full rated capacity.
For a specific device: Size the fuse slightly above the device’s rated current to prevent nuisance blowing, but below the wire’s capacity.
Device draws 12A maximum. Wire is rated 20A. Use a 15A fuse — protects device from sustained overcurrent while well within wire rating.
Practical Application 3: Measuring Resistance
A voltmeter and ammeter together function as an ohmmeter:
Procedure:
- Apply known voltage V to the unknown resistance (don’t use a voltage that would damage it)
- Measure current I with ammeter in series
- Calculate R = V / I
Example: Battery supplies 9V. Ammeter reads 45mA (0.045A). R = 9 / 0.045 = 200Ω
Important caveat: This measures the entire circuit resistance, including wire connections and internal battery resistance. For accurate measurement of just the unknown resistor, use a 4-wire (Kelvin) measurement or ensure the reference voltage is truly the voltage across the unknown element only.
Field application: Testing a suspect component (damaged coil, burned resistor):
- Remove from circuit
- Apply safe test voltage
- Measure current
- Compare R to expected value
A burned resistor usually reads open circuit (infinite resistance) or changes significantly from its marked value. A shorted turn in a coil reduces resistance below normal.
Practical Application 4: Generator Design
Using Ohm’s law to size a generator’s output.
Goal: Build a generator that delivers 12V at 10A (120W).
Load resistance: R_load = V / I = 12 / 10 = 1.2Ω
Generator must produce: Higher than 12V, to account for internal resistance of windings.
If generator winding resistance is 0.5Ω: EMF required = V_terminal + I × R_winding = 12 + 10 × 0.5 = 12 + 5 = 17V
The generator must develop 17V open-circuit to deliver 12V at 10A to the load.
Winding design trade-off: Fewer turns → lower winding resistance → less internal drop → more efficient. But fewer turns also means less EMF. Must balance turns (for voltage) against wire gauge (for resistance).
Practical Application 5: Voltage Divider Design
Using Ohm’s law to set voltage levels.
Goal: Produce 5V from 12V supply for a small circuit drawing negligible current.
Series voltage divider:
- R1 from 12V to output
- R2 from output to ground
- V_out = 12 × R2/(R1+R2) = 5V
Choose values: Let R_total = R1+R2 = 1000Ω R2/(R1+R2) = 5/12 = 0.417 R2 = 0.417 × 1000 = 417Ω → use 390Ω (nearest standard) R1 = 1000 - 417 = 583Ω → use 560Ω
Verify: V_out = 12 × 390/950 = 4.93V ≈ 5V ✓
Current drawn from supply: I = 12/950 = 12.6mA — this is wasted as heat, so choose high total resistance for efficiency, but not so high that load current disturbs the divider.
Ohm’s Law Limitations
Ohm’s Law applies to linear, resistive elements. It breaks down for:
Non-linear elements:
- Diodes: current doesn’t scale with voltage — exponential relationship
- Incandescent bulbs: resistance increases with temperature — cold resistance ≠ hot resistance; bulbs draw 10× more current at startup than at full brightness
- Arc discharges: voltage stays nearly constant over a wide current range
Temperature effects: All real resistors change value with temperature. For copper, resistance increases ~0.4% per °C. A wire that reads 1Ω at 20°C reads ~1.2Ω at 70°C — relevant for fuses and motor windings.
AC with reactive elements: As covered in the impedance article, Ohm’s law in AC circuits uses impedance Z instead of resistance R — Z includes both resistance and reactance.
Remembering the law under stress: The Ohm’s law triangle — draw a circle, put V on top, I×R on bottom divided by a line. Cover the unknown; what’s left is the formula: cover V → I×R. Cover I → V/R. Cover R → V/I.
Drilling Ohm’s law until it’s automatic is one of the most valuable things an electrical worker can do. Almost every practical calculation starts with or passes through V = IR.