Ohm's Law

The fundamental equation of resistance.

Current Flow is Proportionate to Resistance

Going back to the water analogy, we can think of resistance as the valve at the bottom of the water tank:

Illustration of a water pipe with a valve in the center of it, representing a resistor

Given a constant water pressure (voltage), if we put in a valve that was half the size of the pipe, we would expect that the amount of water that flows through would also be divided, proportionally, in half.

This relationship holds true for electricity as well, and is codified in Ohm’s Law; as more resistance is added to a constant voltage circuit, fewer electrons can make it through. The equation for this relationship can be expressed as:

Amperage = Voltage / Resistance

For historical reasons, amperage is often labeled I (for intensity), and sometimes voltage is labeled E (for electromotive force). The most common labeling for Ohm’s law is usually:

I = V/R

But you may also see:

I = E/R

Ohm’s Test Circuit

Consider the following circuit diagram that includes a voltage source and a resistor:

Circuit diagram that shows a circuit loop with a resistor at the top of the loop, and a source voltage at the bottom of the loop.

If the voltage source is 1.5V, and the resistance is 50ohms, we can calculate the amount of amps that can make it through the circuit as:

Amps = I = V / R = 1.5V / 50Ω = 0.03A

From that, we can also calculate the wattage/power as (watts = amps * volts):

Wattage = 1.5V * 0.03A = 0.045W

Rule of Significant Digits

Doing this math brings up an important point, which is the rule of significant digits, which prevents us from stating a computational answer that has more precision than actually intended.

After completing any calculation, it’s necessary to round to the least number of digits in the input numbers.

So for the above calculation, we had inputs of 1.5V and 0.03A and an output of 0.045W. The input numbers both had two significant digits, so we can only have a result of two significant digits, which means we need to round 0.045W to 0.05W. We can ignore the zero left of the decimal when counting significant digits because it’s just a convenience marker to make it clear there is a decimal.

Other Forms of Ohm’s Law

Using algebra, we can solve the equation of Ohm’s law for resistance, or voltage:

Solved for Resistance (R)

R = V / I
ohms = volts / amps

Solved for Voltage (V)

V = I * R
volts = amps * ohms

Ohm’s Law Pyramid

The Ohm’s Law triangle, also known as the power triangle is helpful in remembering the various solutions of Ohm’s law:

Illustration of a triangle divided into three sections with volts in the top and the bottom divided again with amps on the left and ohms on the right

It roughly represents the mathematical relationship of Ohm’s law; it’s divided vertically by a line that indicates division (below V), and horizontally, with a line that stands for multiplication (between I and R).

So to read it, choose any given unit as the solution, and then use the division/multiplication rules of the lines.

Therefore, starting with a solution for V, we have:

V = I * R
volts = amps * ohms

Solving for I:

I = V / R
amps = volts / ohms

And finally, solving for R:

R = V / I
ohms = volts / amps

Online Ohm’s Law Calculator

There is a fantastic Ohm’s law calculator online here.

Next - Calculating Simple Resistance

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