Ohm’s Law (and Circuit Theory) Tutorial
Ohm’s Law is probably the most fundamental law in Electric Circuit Theory. Ohm’s law is a simple formula relating current and voltage through a resistor. In circuit theory, resistors are the building blocks for analysis. Resistors are physically used to resist charge thereby creating a voltage drop across them. This drop can be used to make one voltage source into two separate sources (see a Voltage Divider). Stated below is Ohm’s Law.
where V is the voltage drop across the resistor, I is the current flowing through the resistor, and R is the nominal (constant) resistance of the resistor.
You could think of V as being the dependant variable, I being the independent variable, and R being the slope of the graph. You can see that voltage and current have a linear relationship. The higher the resistance, the steeper the graph, which means that a small increase in current results in a substantial increase in voltage (this implies that for a given current flow, the voltage drop across a higher resistance is larger). The smaller the resistance, the flatter the graph would be which means it takes a larger current to produce a change in voltage. Physically this means that for smaller resistances, there is not a large drop in voltage across them for a given current.
Ohm’s Law by itself is very simple to use, but often we need to analyze more complicated circuits. Usually, we can combine resistors together to simplify the circuits. Before we tackle this problem, two definitions need to be introduced. Resistors can be arranged in a circuit in 3 different ways. The first case is called “series resistances.”
The term “Resistors in Series” means that the end of one resistor is attached to the beginning of the next resistor. You can think of this in terms of cars waiting at a traffic light in a line. The cars line up one behind the other. In a circuit, resistors in series share the same current (remember current is always the same for one branch and resistors that are in series are in the same branch. Current changes when branches form and the current has more than one way to go; some of the current will take one branch, some will take the other branch) however they do not necessarily share the same voltage. Each resistor has its own voltage drop. For another description, think back to science class when you would have several light bulbs in series (a wire connected the battery to the first bulb, then a wire connected the first bulb to the second bulb and so on…). If one bulb broke and would not allow current to flow, all the other lights would not work (since they are all in series if one goes, current can’t reach the others…think of those old Christmas lights). In terms of real life, if the person in front of you broke down and there was only lane, you could not get around them and no traffic would flow.
To combine resistors in series, we merely add the resistors together. It’s very simple.
Another way resistors can be connected together is in parallel. Parallel resistors ends are connected together. This means that the tops of both resistors are connected at a common point and the bottoms of the resistors are connected together (at a different point than the tops of course). This implies the voltage is the same across the two resistors (since their ends are connected all together), but this does introduce the concept of branches. Since the resistors are no longer one right after the other, as is the case for series, when current gets to the two resistors, it has two ways it can go (either through one resistor or the other). This means that the current is not necessarily the same through each resistor. You can think of this in real life as having multiple lanes on a road. Traffic can flow in either lane and still get to the final destination; however one lane may travel faster than the other (the comparison here is speed with current). If one branch breaks down, current (all of the current) will flow through the remaining branch (or braches). Just like in traffic situations, if one lane is impassable, another lane can be used.
Combining resistors in parallel is a little more involved. The most uniform rule is stated below with a schematic to describe what resistors in parallel look like in a circuit.