| layout | default |
|---|---|
| title | L3: Ohm's Law |
| description | Understand Ohm's Law (I = V/R) and its three forms for solving current, voltage, and resistance, with a water-flow analogy and a hands-on CircuitJS activity. |
| image | /electronics/assets/images/PoseuillesLawAndOhmsLaw_FigureByJonFroehlich.png |
| nav_order | 3 |
| parent | Intro to Electronics |
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Figure. Coming up: Ohm's Law (
In this lesson, we will learn about Ohm's Law, one of the most important empirical laws in electrical circuits that describes how current, voltage, and resistance relate together. While Ohm's Law is incredibly useful in analyzing and understanding how circuits work, like many "laws", it is not always obeyed (particularly for what are called "non-ohmic" devices like LEDs or other diodes—which we will explore in Lesson 6: LEDs).
For now, on to Georg Ohm's Law!
In 1827, after years of experimentation, German physicist Georg Simon Ohm published the "Galvanic Circuit Investigated Mathematically", which became the foundation for Ohm's Law. Ohm's Law states that the current (
Thus, if we double the voltage in our circuit—for example, by stacking two batteries together in series—then we will also double the current. Ohm's Law has many implications for how we build and use circuits with microcontrollers, including voltage dividers and resistive sensors.
Importantly, you will see and use Ohm's Law in all three equivalent incarnations (which can be derived with simple algebra):
When you want to solve for current in your circuit, you use:
To solve for voltage, use:
To solve for resistance, use:
Notice how these equations map to the concepts we explained in our first lesson on Voltage, Current, and Resistance—which you may want to return to. For example,
Drawing again on our hydraulic-electric analogies (which we used amply in previous lessons), we can highlight another similarity. In the 1840s, Poiseuille empirically showed that the flow rate of water through a pipe is equal to the pressure drop across the pipe divided by the pipe's resistance—this is called Poiseuille's Law. And it conceptually makes sense: a higher pressure difference between two ends of a pipe creates more force and a lower resistance allows more water flow.
Does this equation sound familiar? It should. It is exactly Ohm's Law! Current flow in a circuit is directly proportional to the voltage drop in a circuit divided by its resistance. See image below.
Figure. Poiseuille's Law for the smooth flow of fluids and Ohm's Law for electric current are similar. Image based on HyperPhysics at Georgia State and created in PowerPoint. Images of Poiseuille and Ohm are from Wikipedia. {: .fs-1 }
{: .note } Poiseuille's Law equation only holds for the smooth (laminar rather than turbulent) flow of a Newtonian fluid like water. But such a stipulation is not relevant to electrical current.
You might be asking, "If
A common "gotcha" in applying Ohm's Law—or analyzing circuits in general—is messing up base units. In digital circuits, we often deal with kilohms (kΩ)—which is 1,000 ohms—milliamps (mA)—which is
For example, if a circuit contains a 2.2kΩ resistor with a 9V battery, to calculate the current do not mistakenly write
So, always make sure you double check your units!
Below, we've written some common SI prefixes—most of which should be familiar to you from other measurement quantities.
| Conversion factor | Scientific notation | Prefix | Abbreviation | English word | Examples |
|---|---|---|---|---|---|
| 1,000,000,000,000 | tera | T | trillion | terabyte, terameter | |
| 1,000,000,000 | giga | G | billion | gigabyte, gigawatt | |
| 1,000,000 | mega | M | million | megabyte, mega-awesome | |
| 1,000 | kilo | k | thousand | kilobyte, kilometer, kilohm | |
| 1 | base unit | gram, meter, amp, volt, ohm | |||
| 0.001 | milli | m | thousandth | millimeter, milliamp, millivolt | |
| 0.000001 | micro | μ | millionth | micrometer, microamp | |
| 0.000000001 | nano | n | billionth | nanosecond, nanoamp | |
| 0.000000000001 | pico | p | trillionth | picosecond, picoamp | |
| {: .fs-1 .condensed-table } |
Table. This chart is based on NIST's Metric SI Prefixes webpage and Figure 2.2 in Bartlett's book. {: .fs-1 }
To convert from a prefixed unit to a base unit, multiply by the conversion factor. To convert from a base unit to a prefixed unit, divide by the conversion factor.
So, for example, to convert 2.2kΩ to ohms, we would multiply by the conversion factor for kilo (k), which is 1,000. So,
Whew, OK, now we are ready to start analyzing some circuits. We'll start with a simple circuit and go from there. When analyzing (or even preparing to build) circuits, it's always a good idea to get out a pencil and paper. So, please do that now.
In addition, it's helpful to have a way to check our work, which we can do in a circuit simulator. I like to use CircuitJS but I have also used EveryCircuit and CircuitLab—the latter costs money.
Before we begin, let's watch this video of me building a simple resistive circuit in CircuitJS and calculating its current, given a voltage source and resistor.
Video. The video was created using the CircuitJS simulator. Direct link is here. {: .fs-1 }
Imagine a battery-powered circuit with a single resistor (basic, yes but pedagogically powerful!). If we are given the voltage
Figure. A simple 9V-powered circuit with a single resistor of
To begin your analysis, you'll want to identify everything that you know about this circuit.
Observe that all wires touching the positive battery terminal have the same electric potential (
And because we are solving for current, we need to use the Ohm's Law formulation:
Figure. All wires touching the battery's positive terminal have the same voltage (9V). Similarly, all wires touching the battery's negative terminal have the same voltage (0V). Images made in Fritzing and PowerPoint. {: .fs-1 }
Having established that all of the wires on the top of the circuit (those directly connected to the positive terminal) are the same electric potential, we can mark it as a single node
Now, we can substitute
Figure. We can call all wires touching the battery's positive terminal node
Finally, we are ready to solve for current
Figure. We successfully applied Ohm's Law to solve for current:
Let's try to solve for current again with a similar circuit. This time the resistance has been increased from
Before doing anything else, it's useful to think conceptually about what will happen.
Current decreases, right? And does so proportionally.
Indeed, the current goes from
Figure. As expected, the current
As noted above, we can use the three different formulations of Ohm's Law (
In this case, let's use Ohm's Law to solve for an unknown voltage source. Assume a similar circuit as before: a single voltage source (but of unknown voltage) with a single resistor of size
Because we are solving for voltage, we should use the
Now, we can easily solve for
Figure. Using the
I bet you're getting the hang of it now!
Finally, you can use
Again, the first thing to do is convert all units to base units. So,
Now, we can solve for
Figure. Using the
Before moving on to the activity, try solving these three problems on your own. Check your work using the formulas above—and pay attention to units!
- A circuit has a 5V battery and a 1kΩ resistor. What is the current?
- A circuit draws 15mA of current through a 330Ω resistor. What is the voltage drop across the resistor?
- A 9V battery produces 4.5mA of current in a circuit with a single resistor. What is the resistance?
{: .note }
Answers. (1)
$$I = \frac{5V}{1000Ω} = 5mA$$ . (2)$$V = 0.015A \times 330Ω = 4.95V$$ . (3)$$R = \frac{9V}{0.0045A} = 2000Ω = 2kΩ$$ .
Now that we've built up an initial understanding of Ohm's Law, it's time to build and play with some circuits in a circuit simulator.
Using CircuitJS, build and analyze five different types of resistive circuits. You can build whatever circuits you want with a few requirements:
- All circuits should have only a single power supply
- You should use only resistors
- You can use as many resistors per circuit as you'd like but double click on the wires to show current/voltage
- For each circuit, take a screenshot and put it in your prototyping journal along with a brief reflection of what you observed/learned.
You can save your circuits in one of two ways: (1) download them locally (File -> Save As) or (2) export them as a shareable link (File -> Export as Link)—use this latter option for your prototyping journals.
In your prototyping journals, include a screenshot of each CircuitJS circuit along with a brief description of what you observed and a link directly back to the CircuitJS circuit that you made.
In this lesson, we learned:
-
Ohm's Law is an empirical law that describes the linear relationship between voltage, current, and resistance:
$$I = \frac{V}{R}$$ - This law builds on the concepts and intuitions we developed in Lesson 1, and can be rearranged to solve for any one of the three quantities given the other two
- A common "gotcha" for beginners is forgetting to convert measurements to base units (volts, amps, ohms) before applying Ohm's Law
- We applied Ohm's Law to simple single-resistor circuits and verified our calculations using CircuitJS
-
Introduction to Ohm's Law, Khan Academy
-
What is Ohm's Law?, Math and Science
In the next lesson, we will apply Ohm's Law to more complex circuits—specifically those that combine resistors in series and those that combine them in parallel.