| Symbol | Variable | SI Unit | Typical Range |
|---|---|---|---|
| V | Voltage (EMF) | Volts (V) | 0.001 V – 765,000 V |
| I | Electric Current | Amperes (A) | 1 μA – 10,000 A |
| R | Resistance | Ohms (Ω) | 0.001 Ω – 10 MΩ |
- Applies to DC circuits and resistive AC loads only (purely resistive, no reactance)
- Assumes linear, time-invariant resistance — does not apply to non-linear components (diodes, transistors, varistors)
- Does not account for temperature coefficient of resistance (resistance changes with temperature)
- Not valid for superconductors (zero resistance) or plasma states
- For AC circuits with capacitors or inductors, use impedance (Z) in place of resistance (R)
- Results assume ideal conditions — real-world values will vary due to component tolerances
What Is Ohm’s Law?
Ohm’s Law is the most fundamental relationship in electrical engineering. Formulated by Georg Simon Ohm in 1827, it defines the linear relationship between voltage, current, and resistance in an electrical circuit. The law states that the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance — provided temperature and other physical conditions remain constant.
Ohm’s Law is used in virtually every electrical and electronic design — from sizing wire gauges to designing voltage regulators, calculating power dissipation, and troubleshooting circuit faults.
The Ohm’s Law Formulas
- V — Voltage in Volts (V). The electrical potential difference driving current flow.
- I — Current in Amperes (A). The rate of charge flow through the conductor.
- R — Resistance in Ohms (Ω). Opposition to current flow.
The Power Equations
Combining Ohm’s Law with P = V × I yields three essential power formulas used in every electrical design:
Worked Examples
Example 1 — Automotive Circuit (Solving for Current)
A 12V automotive battery powers a resistive heating element with a resistance of 4.7 Ω. What current flows through the circuit and what is the power dissipated?
Example 2 — LED Current Limiting Resistor (Solving for Resistance)
You want to run a red LED (forward voltage 2.0V, desired current 20mA) from a 5V supply. What resistor value is needed?
Example 3 — Industrial Motor Circuit (Solving for Voltage Drop)
A 120V motor draws 8.5A through 50 feet of 14 AWG copper wire (resistance ≈ 0.00308 Ω/ft, round trip = 100 ft). What is the voltage drop in the wire and what voltage does the motor actually see?
Example 4 — Resistor Power Rating Check
A 1 kΩ resistor is connected across a 24V supply. What power is it dissipating and is a 1/4W resistor adequate?
Example 5 — Battery Internal Resistance
A 9V battery measures 8.7V under a 100 mA load. What is the battery’s internal resistance?
Real World Applications
Common Mistakes Engineers Make
Frequently Asked Questions
Ohm’s Law (V = IR) applies directly to purely resistive AC loads. For AC circuits containing capacitors or inductors, you must use impedance (Z) instead of resistance: V = IZ. Impedance accounts for the phase shift between voltage and current in reactive components and is calculated as Z = √(R² + X²), where X is reactance.
Most conductors have a positive temperature coefficient — resistance increases as temperature rises because thermal energy causes more atomic vibrations that impede electron flow. Use R(T) = R₀[1 + α(T − T₀)] where α is the temperature coefficient. Copper: α ≈ 0.00393/°C. Some materials (like carbon and semiconductors) have negative temperature coefficients — resistance decreases as temperature rises.
Resistance (R) opposes current flow equally regardless of frequency and dissipates energy as heat. Impedance (Z) is the total opposition to AC current and includes resistance plus reactance (from capacitors and inductors). Reactance is frequency-dependent — capacitive reactance decreases with frequency, inductive reactance increases. At DC (0 Hz), impedance equals resistance.
In a parallel circuit, each branch has the same voltage but different currents. Calculate current in each branch using I = V/R for that branch’s resistance. Total current is the sum of all branch currents. Equivalent parallel resistance: 1/R_total = 1/R1 + 1/R2 + … For two parallel resistors: R_total = (R1 × R2) / (R1 + R2).
Kirchhoff’s Voltage Law (KVL) states that the sum of all voltage drops around any closed loop equals the sum of all voltage sources. Ohm’s Law provides the tool to calculate the voltage drop across each resistive element in that loop: V = IR. Together, KVL and Ohm’s Law form the foundation for analyzing any DC circuit with multiple components.
Ohm’s Law is extremely accurate for metallic conductors (copper, aluminum, steel) at normal operating temperatures and current densities. It begins to deviate at very high temperatures (near melting point), very high current densities (approaching conductor limits), or in superconducting materials. For practical engineering calculations on standard conductors, Ohm’s Law is reliable to within 1-2% when accurate resistance values are used.