Ohm's Law
What is the Ohm's Law?
Ohm's Law states that the voltage across a conductor is directly proportional to the current flowing through it, with resistance as the constant of proportionality. It's the foundational relationship for analyzing electrical circuits ā nearly every circuit problem in an introductory electronics or physics course eventually comes back to this one equation, or one of its combined forms with the power formula.
Georg Ohm published this law in 1827, based on careful experiments measuring how current varied with the length and thickness of wires he tested. It was initially met with skepticism from the German scientific establishment, but was later confirmed and became so fundamental that the unit of electrical resistance ā the ohm ā was named after him.
A useful mental model: voltage is like the pressure pushing charge through a circuit, current is the actual flow of that charge, and resistance is whatever opposes the flow ā a wider pipe (lower resistance) lets more flow through for the same pressure, exactly the way a thicker wire allows more current for the same voltage. This water-pipe analogy breaks down at a deep physical level, but it's a genuinely useful way to build intuition for how the three variables relate.
What Each Variable Means
When to Use It
- Finding the voltage across a component when current and resistance are known
- Finding the current through a component when voltage and resistance are known
- Analyzing simple electrical circuits
Step-by-Step Examples
Example 1: Finding voltage
Problem: A circuit has a current of 2 A flowing through a resistor of 15 Ī©. What is the voltage?
Current and resistance are both given.
I = 2 A, R = 15 Ī©Multiply current by resistance.
V = 2 Ć 15Example 2: Finding current
Problem: A 12 V battery is connected across a 4 Ī© resistor. What current flows?
Solve V = IR for current.
I = V / RDivide voltage by resistance.
I = 12 / 4Interactive Calculator
Solving for Other Variables
I = V / RSolve for current when voltage and resistance are known.R = V / ISolve for resistance when voltage and current are known.Common Mistakes
Mistake: Mixing up which variable to solve for without rearranging first.
Fix: Write V = IR down, then algebraically isolate whichever variable is unknown ā don't try to guess the rearranged form from memory.
Mistake: Using inconsistent units (e.g. milliamps instead of amps).
Fix: Convert current to amperes and resistance to ohms before applying the formula, or convert the final voltage answer to account for the units actually used.
Practice Questions
A resistor of 10 Ī© has 3 A flowing through it. Find the voltage.
A 12 V battery is connected to a 4 Ī© resistor. Find the current.
Hint: Rearrange V = IR to solve for I.
Frequently Asked Questions
Does Ohm's Law apply to every electrical component?
No ā it holds for "ohmic" conductors, where resistance stays constant regardless of voltage or current. Components like diodes and transistors are non-ohmic, and their V-I relationship isn't a straight line.
How is Ohm's Law used with electrical power?
Combined with P = IV, you can substitute Ohm's Law to get two more power formulas: P = IĀ²R and P = VĀ²/R ā useful when only some of the circuit's values are known.