Ohm's Law
Ohm's Law is one of the most fundamental relationships in electrical circuits, describing the relationship between voltage, current, and resistance. It provides the foundation for understanding how electrical circuits behave and is essential for circuit analysis and design.
Statement of Ohm's Law
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.
- Where:
- \(V\) = voltage (volts, V)
- \(I\) = current (amperes, A)
- \(R\) = resistance (ohms, Ω)
- Linear relationship: Voltage is directly proportional to current
- Ohmic materials: Materials that obey Ohm's Law
- Non-ohmic materials: Materials that don't follow this linear relationship
Alternative Forms
Ohm's Law can be rearranged to solve for any of the three variables, depending on what's known and what needs to be calculated.
Use this pyramid to help you if you are ever confused. The Ohm’s Law pyramid helps you quickly find formulas by covering the quantity you want: cover V to get V = I × R, cover I for I = V ÷ R, and cover R for R = V ÷ I. It’s a simple way to remember how voltage, current, and resistance relate without memorizing each formula separately.
- Current calculation: \(I = \frac{V}{R}\)
- Resistance calculation: \(R = \frac{V}{I}\)
- Power relationship: \(P = VI = I^2R = \frac{V^2}{R}\)
Ohmic vs Non-Ohmic Materials
Ohmic Materials
- Linear relationship: \(V = IR\) holds true
- Examples: Most metals (copper, aluminum, gold)
- Temperature range: Linear over a wide temperature range
- Graph: Straight line through origin on V-I plot
Non-Ohmic Materials
- Non-linear relationship: \(V = IR\) doesn't apply
- Examples: Diodes, transistors, light bulbs (at high current)
- Behavior: Resistance changes with current or voltage
- Graph: Curved line on V-I plot
Memory Trick: VIR Triangle
Remember Ohm's Law using the VIR triangle:
- V = Voltage (top of triangle)
- I = Current (bottom left)
- R = Resistance (bottom right)
To find any variable:
- V = I × R (multiply the two bottom values)
- I = V ÷ R (divide top by bottom right)
- R = V ÷ I (divide top by bottom left)
This visual triangle helps you quickly rearrange the formula!
Worked Examples
Example 1: Basic Ohm's Law
Problem: A 12 V battery is connected to a 4.0 Ω resistor. What is the current flowing through the resistor?
Solution:
- Ohm's Law: \(I = \frac{V}{R}\)
- Substitution: \(I = \frac{12 \text{ V}}{4.0 \text{ Ω}}\)
- Calculation: \(I = 3.0 \text{ A}\)
Answer: The current is 3.0 A.
Example 2: Resistance Calculation
Problem: A circuit draws 2.5 A when connected to a 6.0 V source. What is the resistance of the circuit?
Solution:
- Ohm's Law: \(R = \frac{V}{I}\)
- Substitution: \(R = \frac{6.0 \text{ V}}{2.5 \text{ A}}\)
- Calculation: \(R = 2.4 \text{ Ω}\)
Answer: The resistance is 2.4 Ω.
Ohm's Law Interactive
Explore the relationship between voltage, current, and resistance: