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Electrical & Instrumentation

Ohm's Law Explained

Ohm's Law relates voltage, current, and resistance in a DC or purely resistive circuit: V = IR. Learn the three forms of the equation, common units, and when to use each.

TypeEngineering guide — concept explainer

Definition

Ohm’s Law states that the voltage across a conductor is directly proportional to the current flowing through it, with the constant of proportionality being the resistance. In its simplest form: V = I x R. It applies to DC circuits and purely resistive elements — components where current and voltage are in phase and there is no reactive (capacitive or inductive) behaviour.

Why it matters

Ohm’s Law is the most fundamental relationship in electrical and instrumentation engineering. It governs every resistive element in a circuit: from instrument loop wiring to heater elements and shunt resistors. Understanding this relationship is essential for troubleshooting 4-20 mA loops, sizing dropping resistors, checking cable resistance, and interpreting voltage measurements across known loads.

Formula

Voltage
V = I x R
Current
I = V / R
Resistance
R = V / I

Units involved

  • •V (volts) — voltage, also called potential difference or electromotive force
  • •I (amperes, A) — current, the flow of electric charge
  • •R (ohms, Ω) — resistance, opposition to current flow

Concept diagram

VRIV = I x RVoltage = Current x Resistance

Worked example

A 24 V power supply drives current through a 250 Ω precision resistor (commonly used to convert a 4-20 mA signal to a 1-5 V signal). What is the current at full scale?

  1. 01V = 24 V, R = 250 Ω
  2. 02I = V / R
  3. 03I = 24 / 250
  4. 04I = 0.096 A = 96 mA
Result

The current through the 250 Ω resistor at 24 V is 96 mA.

Common mistakes

  • •Applying Ohm’s Law to AC circuits with reactive components (capacitors, inductors) without accounting for impedance. Ohm’s Law in its V = IR form is for DC or purely resistive loads only.
  • •Confusing resistance with impedance. Impedance includes both resistance and reactance and requires complex-number (phasor) analysis.
  • •Forgetting unit prefixes. Mixing mA with A or kΩ with Ω introduces errors of 1,000x.
  • •Assuming resistance is constant regardless of temperature. Wire resistance changes with temperature — see the RTD guide for how this is exploited in temperature measurement.

When to use the calculator

Use the Ohm’s Law calculator to quickly find any one of voltage, current, or resistance when you know the other two. It handles unit prefixes (mV, mA, kΩ) and shows all three forms of the equation.

Ohm's Law Calculator →Electrical Power Calculator →

FAQ

Does Ohm’s Law apply to AC circuits?
In a purely resistive AC circuit (e.g., a heating element), V = IR still holds for RMS values. However, if the circuit contains capacitors or inductors, you must use the generalised form V = IZ, where Z is the complex impedance. This calculator covers the resistive case only.
What is the relationship between Ohm’s Law and power?
Combining Ohm’s Law with the power formula (P = VI) gives P = I²R and P = V²/R. These derived forms are covered in the Electrical Power guide.
Why is a 250 Ω resistor so common in instrumentation?
A 250 Ω resistor converts a 4–20 mA signal to a 1–5 V signal, which is a standard input range for many PLCs and DCS analogue input cards. At 4 mA: V = 0.004 × 250 = 1 V. At 20 mA: V = 0.020 × 250 = 5 V.
Is Ohm’s Law valid for semiconductors?
Semiconductors (diodes, transistors) are non-linear — their resistance changes with voltage and current. Ohm’s Law applies only to linear, ohmic conductors where resistance is constant over the operating range.