 # Ohm’s Law Tutorial with Easy Practice Problems

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Ohm’s Law is a foundational equation in basic circuits and is amazing in its simplicity and its usage. In this tutorial, we’re going to learn about what Ohm’s Law is, where you can and can’t use it, and do a few examples of very, very simple circuits.

Ohm’s Law establishes a relationship between voltage and current through a linear resistance. In the tutorial defining and relating voltage, current, resistance, and power, we used water as an example. Thinking of that analogy, it probably isn’t surprising that there is a mathematical relationship between how much water flows depending on the height of the head of water and the size of the pipe. For electricity, that relationship is established as:

or

A few important notes:

• This means that the voltage divided by the resistance gives you the current flow. Or, the height of the water divided by the size of the pipe, gives you the water flow. Intuitively, this should make sense. As you go to a higher potential, more current will want to flow. If you increase the size of the pipe by decreasing the resistance, more current will flow. And the inverse is true.
• This is a linear equation. Not only does this mean that the relationship is a straight line, but if you are dealing with something that is non-linear, where resistance changes depending on the voltage, this equation does not apply. That is uncommon so we’ll assume resistors are linear unless explicitly stated otherwise.
• This holds when you have a voltage and a resistance (usually a resistor), but as we learn about other components and power sources, this law does not typically apply to them.

Voltage and current can both be positive or negative. As mentioned in the previous tutorial, voltage is relative, so a negative voltage is just at a lower potential than what is (perhaps arbitrarily) established as zero volts or ground. Current, being a measurement of flow, is positive or negative depending on which way you, or the problem, assigns the flow. If you say that the current is flowing from A to B, and the current is actually flowing from B to A, then that current is negative. However, if you look at the same situation and reference the current as flowing from B to A, then when current does flow from B to A, it is a positive current flow! This can be really confusing at first and both of these still trip me up if I haven’t done any circuit problems for awhile. The most important thing to keep these straight is to draw out your assumptions of voltage potential and current flow and make sure that the equations you use match those assumptions. We’ll review this concept in some of the practice problems at the end of this tutorial.

There are two common extremes that you can see in Ohm’s Law in regards to resistance. When resistance is zero and when resistance is infinite. When resistance is zero, basically when a wire is connecting two different voltage potentials, this is called a short circuit. It’s shorting the voltages together. Looking at Ohm’s Law, when resistance is zero, if you have any finite voltage, you get an infinite current. While there’s no such thing as an infinite current in real life, if this isn’t planned, the current will be high enough to cause some damage!

The other extreme is when resistance is infinite, or when two voltage potentials are completely and utterly separated. Depending on the circumstances, sometimes you can consider extremely high resistances as being infinitely large but use that assumption carefully. When a resistance is infinite, it means that, no matter the voltage, there is no current. If this is desired, then great. If not, it usually means that something that is expecting power isn’t getting it.

Final Items of Note

You will sometimes hear about two other related but different terms. The first of these terms is resistivity. Resistivity is a property of a material and is the basis of resistance. A highly conductive material will have a very low resistivity (like copper) while a highly insulative material will have a very high resistivity (like rubber). Most materials used for a resistor will be somewhere in the middle. Once you know the length and cross sectional area of the material, you can multiply the resistivity by the length and divide it by the cross sectional area.

R - Resistance (Ω)
ρ - Resistivity (Ω-cm or Ω-m)
l - Length (cm or m)
A
- Cross-sectional Area (cm2 or m2)

If you take a moment to look at this equation, it should make sense intuitively. As you increase the length, the resistance will go up. If you make the area that the electrons can pass through larger, the resistance will go down.

The second term is conductivity, G. This is simply the inverse of resistance. It is used in certain cases but compared to resistance, is extremely uncommon. The units are sometimes called “mhos” with an upside down omega symbol compared to “ohms” with its right-side up omega symbol. On occasion, these are also called Siemens.

You get an inverted Ohm’s law with this as well:

## Example / Practice Problems #### Problem 1. Node A: 1000V to Node B: 0V, across a 100 ohm resistor.

Solution:

In this first practice problem, we establish the voltage drop across the resistor and setup the equation. Node A is 1000 volts and Node B is 0 volts, so we can setup the equation as 1000V - 0V, and then divide it by the resistance, which is 100 ohms. So we get:

So we get 10A of current flowing from Node A to Node B. #### Problem 2. Node A: 12V to Node B: 3V, across a 200 ohm resistor.

Solution:

In this second practice problem, we follow the exact same steps as in problem one but have different numbers. We look at the voltage drop from Node A to Node B and setup the first part of the equation, which is 12V - 3V. Dividing it by the resistance, we get the final equation:

In this case, we get 45 milliamps flowing from Node A to Node B. #### Problem 3. Node A: 16V to Node B: 24V, across an 800 ohm resistor.

Solution:

In this third practice problem, due to the fact that we’re still using the terms Node A and Node B, we’ll still setup the equations in reference to flow being from Node A to Node B, even though, by inspection, we can tell that Node B is at a higher voltage potential. It’s okay, because as long as we label everything properly, the answer will still be right. So we have 16V - 24V and then divide that by 800 ohms.

So we get negative 10 milliamps from Node A to Node B. This makes sense because Node B is at the higher voltage so, if we define the current going from A to B, if the current is actually going from B to A, then the current is negative. #### Problem 4. Node A: -7V to Node B: -13V, across a 1.2K ohm resistor.

Solution:

In this fourth and final practice problem we’re going to do, we will still define the problem in terms of current flowing from Node A to Node B. So, once again, we setup the equation. (-7 - (-13))/1200.

Note that, since we’ve been consistent in defining things, we know that the only change with this compared to the last three problems is that we’re subtracting a negative number, thus adding it. Again, since voltages are relative, the actual voltages don’t matter as much as the difference between them. If you want to prove it to yourself, do this problem again with Node A at 6V and Node B at 0V.

## Summary

Ohm’s Law is the foundation of most circuit analysis and is quite simple as long as you carefully pay attention to make certain that the way you setup your equations matches the way you’ve assigned the polarities and flows in the program.

Short circuits and open circuits are extremely common scenarios in both academia and real-life, so it’s good to make those second nature to your understanding of circuits.

Next, we will learn about branches, nodes, and loops, as well as how components can be put in series and parallel. This will allow us to apply Ohm’s Law across a significantly wider, and more practical, array of practical circuits.  