Ohm's Law

The Formula

With Joule's Law of heating, electrical power is calculated as:

Who Discovered Ohm's Law?

Georg Simon Ohm (1789 – 1854), a German physicist and mathematician, published the law in 1827 in his book Die galvanische Kette, mathematisch bearbeitet (The Galvanic Circuit Investigated Mathematically). Despite initial skepticism, his work became the foundation of circuit analysis.

The unit of resistance — the ohm (Ω) — is named in his honor.

Formula Wheel

What Is Ohm's Law?

Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across those two points, and inversely proportional to the resistance. The constant of proportionality is the resistance R:

V = I × R

The law applies to ohmic conductors — materials whose resistance stays constant over the operating range. Metals at constant temperature are ohmic; diodes, transistors, and other semiconductors are non-ohmic.

Understanding V, I, and R

• Voltage (V): the electrical potential difference between two points, measured in volts. Think of it as the "pressure" pushing electrons through a circuit.
• Current (I): the flow of electric charge, measured in amperes. The amount of charge passing a point per second.
• Resistance (R): the opposition to current flow, measured in ohms. A higher resistance means less current for the same voltage.

Quick Example

A 12 V battery is connected to a 4 Ω resistor. What is the current?

Power dissipated by the resistor:

Common Examples

Real-World Applications

1. Circuit Design

Engineers use Ohm's Law to choose resistor values, calculate voltage drops, and verify current limits in analog and digital circuits.

2. Power Supplies

Power supply sizing relies on P = V × I to choose transformers, fuses, and wire gauges.

3. Battery and Solar Design

Battery capacity, solar panel output, and load matching all use Ohm's Law and power formulas.

4. Electrical Wiring

Electricians calculate branch-circuit current to size wiring and overcurrent protection per electrical codes.

5. Electronics Troubleshooting

Technicians use Ohm's Law to predict expected voltages and currents, then compare with measurements.

6. Heating and Lighting

Heater and lamp design uses P = V² / R to choose resistance values for desired power dissipation.

Limitations

• Non-ohmic devices: diodes, transistors, and incandescent bulbs change resistance with operating point or temperature.
• AC reactive circuits: for AC with capacitors or inductors, use impedance Z = √(R² + X²) instead of R alone.
• Non-linear media: arcs, plasma, and semiconductors deviate significantly.

Common Mistakes

• Mixing up units: voltage in mV, current in mA, and resistance in kΩ gives wrong results without conversion.
• Confusing power formulas: use P = I² × R only with the current through R, not the source current.
• Forgetting load resistance changes with temperature: filaments and thermistors are non-linear.
• Applying to AC reactive circuits: must use impedance, not just resistance.

Frequently Asked Questions

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