Basic Resistor Circuits
There are usually multiple paths through an electrical circuit. In order to understand how to calculate the current in a circuit, we have to know where the resistors are located and how they are connected.
Resistors in Series
First, let’s look at a circuit with two resistors in series. There is only one path through this circuit, so the current is equal to the voltage divided by the total resistance.
I = V / Rtotal
The total resistance measured over the two resistors = 326 ohms + 1467 ohms.
Always use the same units when you add resistance values. When working with other formulas, it is useful to use ohms rather than kilo ohms or milli ohms.
Resistors in Parallel
When resistors are in parallel, the current is divided between two or more paths. Therefore, each resistor only resists part of the current, so the total effective resistance in the circuit is less than either resistor by itself. We can calculate resistance, but it is easier to remember than the inverse of resistance, which is conductance, adds between the two parallel resistors.
Conductance is a measure of how much a component allows current to flow. It is the reciprocal of resistance, which is how much a component opposes the flow of current. The Conductance, G = 1 / R and is measured in the unit siemens.
Gtotal = G1 + G2 or
So, if you look at the total resistance, you take the reciprocal of Gtotal.
The total resistance of this circuit is 1 divided by (1/981 + 1 / 1793).
Can you find the total resistance in this circuit?
You can calculate the resistance of the parallel resistors, then add the single resistor in series.
1 divided by (1 / 981 + 1 / 1467) = 588 ohms
Rtotal = 588 + 326 = 914 ohms
You can use the same idea to calculate the resistance in this circuit.
Note, the resistance of the two parallel resistors will always be less than either resistor, but in this case, the parallel resistance will be closer to the value of 326 ohms than it was for R2 in the previous circuit. (588 ohms vs. 981 ohms).
Parallel resistance = 1 divided by (1 / 326 + 1 / 981) = 245 ohms
Total resistance = 1467 + 245 = 1712 ohms
You can practice more resistance calculations at AllAboutCircuits.com
We also learned two very important laws of conservation.
Kirchhoff’s Current Law
Kirchhoff’s Current Law states that at any point on the circuit, the current flowing into a junction will be equal to the current leaving that point. Therefore, when two paths are present, the majority of the current will take the path with the least resistance and the remaining current will travel the paths with more resistance. The total current (for all the paths) will be the same as the original current, before it was divided.
I = I1 + I2 + I3 where each partial current can be calculated as Voltage / Resistance.
Remember also that the voltage across alternate paths will be the same.
Kirchhoff’s Voltage Law
The second of Kirchhoff’s laws states that the total voltage supplied by the battery will be equal and opposite to the total of the voltage drops across each component of the circuit.
Ebattery = E1 + E2 + E3 + E4
Keep in mind that the voltage drops of E1 - E4 are opposite in direction to the voltage supply. So, technically Etotal + E1 +E2 + E3 + E4 = 0
So, putting two resistors in series drops the voltage across the second resistor. This is called a Voltage Divider. One way to reduce the voltage is by using resistors, but a better way to reduce the voltage to part of a circuit is to use resistive diodes. We will talk about diodes later, but basically, they do not allow current to flow in the reverse direction.
Let’s take a look at some actual circuits and what we can get them to do.
Here is a circuit made with snap together components.
The two green components on the right and left are switches.
Switch 1 on the right allows current to flow to the fan driven by a small motor. From there, there are two paths to ground, through the light bulb (involves resistance) or through switch 2, which short circuits the light bulb and reduces the resistance in the circuit.
When you close switch one, the fan will begin to turn and the light bulb will come on. When you close switch two, the fan will turn faster, because more voltage is applied to the motor and the light will turn off.
The second picture shows the light bulb turned on and the fan running.
Let’s look at another circuit.
In this circuit, U1 represents an integrated circuit that plays music. We don’t know a lot about it. The red component is a speaker. On the right is a green switch (1) that plays music one time. On the left is the green doorbell switch (2). Each time you press switch 2, music will play one time.
In this circuit, the resistor has been removed and the doorbell switch has been moved to a different input to U1. In this circuit, you must keep the switch 2 pressed in order to hear the music.
In this circuit, an alarm sounds when the switch 1 is turned on.
Component U2 is like a siren, but there are other sounds it can make.
What happens when you remove the resistor?
In this circuit, U3 makes different laser beam sounds when you use switch 1 or switch 2. The circuit inside U3 allows different combinations of paths to play different sounds. You can press both switches at once for more different sounds.
In this complicated circuit, the LED and light bulb alternate lighting up. At first, the LED went from bright to dim, but then after a little time, it would switch on and off. Can you explain what happened over time?
This circuit demonstrates a periodic switching. You can also put a speaker in instead of the LED and the light bulb and interrupted music from U1 make some eerie space music.
The SNAP kit electronics are very easy to use for demonstrating a lot of different circuits. Unfortunately, we don’t get to see a lot of the math that is going on behind the scenes! Next week, maybe we can try to assemble some of these circuits using a breadboard to connect components.