Ohm's Law Formula: V=IR Explained with Examples
What Is Ohm's Law?
Ohm's Law is the most fundamental relationship in electrical engineering. Discovered by German physicist Georg Simon Ohm in 1827, it states that the electric current flowing through a conductor between two points is directly proportional to the voltage across those two points and inversely proportional to the resistance of the conductor.
In practical terms, this means:
- Double the voltage across a resistor and the current doubles.
- Double the resistance and the current is cut in half.
- The relationship holds at constant temperature for ohmic conductors (metals, most resistors, and carbon film).
Ohm's Law applies to DC circuits directly and to AC circuits when impedance replaces resistance. It is essential for sizing wires, calculating voltage drops, designing HVAC control circuits, and selecting motor starters.
The Core Formula: V = IR
The equation V = IR has three variables:
| Symbol | Quantity | Unit | Measures |
|---|---|---|---|
| V | Voltage | Volts (V) | Electrical "pressure" pushing current through a circuit |
| I | Current | Amperes (A) | Flow rate of electric charge through the conductor |
| R | Resistance | Ohms (Ω) | Opposition to current flow in the conductor |
Ohm's Law Triangle Diagram
The easiest way to remember all three forms is the VIR triangle:
┌─────┐
│ V │
│─────│
│ I × R│
└─────┘
How to use the triangle: Cover the variable you want to find.
- Want V? Cover V → V = I × R
- Want I? Cover I → I = V ÷ R
- Want R? Cover R → R = V ÷ I
The Power Formulas
Power (P) measures the rate at which electrical energy is converted to heat, light, or mechanical work. Measured in watts (W), it combines with Ohm's Law to give three useful formulas:
| Formula | When to Use | Known Values |
|---|---|---|
| P = V × I | You know voltage and current | V, I |
| P = I² × R | You know current and resistance | I, R |
| P = V² ÷ R | You know voltage and resistance | V, R |
Power Triangle
┌───────────┐
│ P │
│───────────│
│ V × I │
└───────────┘
Cover P to get P = VI, cover V to get V = P/I, cover I to get I = P/V.
Worked Examples — DC Circuits
Example 1: Find Current (Simple Resistor)
Problem: A 12V battery is connected to a 4Ω resistor. What current flows?
Solution: I = V / R = 12V / 4Ω = 3 A
Power: P = V × I = 12 × 3 = 36 W
Example 2: Find Voltage (Motor Winding)
Problem: A DC motor draws 8A through a 6Ω winding resistance. What is the voltage drop?
Solution: V = I × R = 8A × 6Ω = 48 V
Power: P = I²R = 8² × 6 = 384 W
Example 3: Find Resistance (LED Circuit)
Problem: An LED operates at 2V and 20mA from a 5V supply. What series resistor is needed?
Solution: R = V / I = (5V − 2V) / 0.020A = 150 Ω
Power dissipated by resistor: P = I²R = 0.020² × 150 = 0.06 W (a ¼W resistor is fine)
Example 4: Find Power (Baseboard Heater)
Problem: A 240V baseboard heater draws 10A. What is its power and resistance?
Power: P = V × I = 240 × 10 = 2,400 W (2.4 kW)
Resistance: R = V / I = 240 / 10 = 24 Ω
Worked Examples — AC Circuits
In AC circuits, impedance (Z) replaces resistance. Impedance combines resistance (R) with inductive reactance (XL) and capacitive reactance (XC):
Z = √(R² + (XL − XC)²)
And the power formula includes the power factor (cos φ):
P = V × I × cos φ
Example 5: Single-Phase AC Motor
Problem: A 240V AC motor draws 15A with a power factor of 0.85. What is the real power?
Solution: P = V × I × cos φ = 240 × 15 × 0.85 = 3,060 W (3.06 kW)
Apparent power: S = V × I = 240 × 15 = 3,600 VA
Reactive power: Q = √(S² − P²) = √(3600² − 3060²) ≈ 1,892 VAR
Example 6: Three-Phase AC System
Problem: A 480V three-phase motor draws 20A per line with 0.90 power factor. What is the real power?
Solution: P = √3 × VL × IL × cos φ = 1.732 × 480 × 20 × 0.90 = 14,965 W (≈15 kW)
Example 7: HVAC Blower Motor
Problem: A 230V blower motor has a winding resistance of 5.75Ω and draws 12A. Find the impedance and power factor.
Solution: Z = V / I = 230 / 12 = 19.17Ω
Power factor: cos φ = R / Z = 5.75 / 19.17 = 0.30
Real power: P = V × I × cos φ = 230 × 12 × 0.30 = 828 W
Ohm's Law for HVAC Applications
HVAC technicians use Ohm's Law daily for:
- Compressor diagnosis: Measure winding resistance to detect open or shorted windings. A locked-rotor current test uses I = V/R.
- Contactor coil verification: A 24V coil with 20Ω resistance should draw I = 24/20 = 1.2A. If current is higher, the coil is shorted.
- Voltage drop calculation: For a 10A load on 50 ft of 12 AWG wire (1.588 Ω/1000 ft), Vdrop = I × R = 10 × (2 × 50 × 1.588/1000) = 1.59V.
- Heating element sizing: A 5 kW, 240V element: R = V²/P = 240²/5000 = 11.52Ω.
- Troubleshooting circuits: If voltage is present but current is zero, the circuit is open (infinite resistance). If current is very high, resistance is low (short circuit).
Quick Reference Table
| Find | Using V & I | Using V & R | Using I & R |
|---|---|---|---|
| Voltage (V) | — | — | V = I × R |
| Current (I) | — | I = V / R | — |
| Resistance (R) | R = V / I | — | — |
| Power (P) | P = V × I | P = V² / R | P = I² × R |
Standards Reference
- IEC 60071 — Insulation Co-ordination (voltage levels and clearances)
- IEEE 141 — Recommended Practice for Electric Power Distribution for Industrial Plants (Red Book)
- NEC Article 210 — Branch Circuits (conductor sizing based on current)
- NFPA 70E — Electrical Safety in the Workplace
Frequently Asked Questions
What is Ohm's Law formula?
Ohm's Law states that voltage (V) equals current (I) multiplied by resistance (R): V = IR. From this single relationship you can derive I = V/R and R = V/I. The related power formulas are P = VI, P = I²R, and P = V²/R.
What are the three forms of Ohm's Law?
The three forms are: V = IR (voltage equals current times resistance), I = V/R (current equals voltage divided by resistance), and R = V/I (resistance equals voltage divided by current). These are algebraic rearrangements of the same relationship.
Does Ohm's Law apply to AC circuits?
Yes, but with modification. In AC circuits, resistance (R) is replaced by impedance (Z), which includes resistance, inductive reactance (XL), and capacitive reactance (XC). The formula becomes V = IZ, and power calculations require the power factor (cos φ): P = VI cos φ.
What is the difference between Ohm's Law and the power formula?
Ohm's Law (V = IR) relates voltage, current, and resistance. The power formula (P = VI) relates power, voltage, and current. They are often combined: since V = IR, substituting gives P = I²R and P = V²/R. You need both to fully characterize a circuit.
Who discovered Ohm's Law?
Georg Simon Ohm (1789–1854), a German physicist, published the relationship in 1827. His work demonstrated that the current through a conductor is directly proportional to the voltage across it, at constant temperature. The unit of resistance (ohm, Ω) is named after him.