We now already understand the meaning of resistance, capacitance, voltage, and current. Every circuit needs some amount charge to flow in it to function. This need or requirement of current in the circuit is called current requirement. Whenever we apply a voltage to a circuit, the circuit uses/eats or draws current which is equal to voltage applied divided by the total resistance in the circuit. Or 1/R times the voltage applied where R is representative of resistance.
While building your circuit, sometimes you will realize that two different sensors in your circuit have two different types of current requirements; other times you have different voltage requirements. Think of this as the different tactics you use to avoid cleaning the room. In such conditions, we use resistors and capacitors in various combinations to get the desired results.
When you have a friend playing with you, isn't it more difficult for you to stop playing and start cleaning, since while you have to clean the house, your friend gets to play? (So unfair!)
A series connection is characterized by all the components connected in a long chain from one terminal of the battery to the other as shown in the diagrams. (Recall from the preceding sections that current flows from the positive terminal of the battery to the negative.)
The following diagram shows resistors R1 and R2 that are connected in a series:
The total resistance in a series circuit is determined by adding all the individual resistances connected in series. Let's get back to the water analogy. The following diagram shows a pump that is pumping water in a water circuit:
Image source: https://ece.uwaterloo.ca/~dwharder/Analogy/Resistors/
The pipe consists of two sand filters. Since each of the sand filters is going to restrict the flow of water according to the density of the sand on the sand filter, the total resistance going to be offered will be the sum of the individual restrictions. Since restriction here is analogous to resistance in electric circuits, in a circuit with series resistance, the total resistance offered to the circuit is going to be the sum of individual resistances. The current across the resistors remains the same the but voltage gets divided.
Total resistance of the circuit here is R = R1+R2+R3.
The following diagram shows capacitors C1 and C2 connected in series:
Coming back to the water analogy, consider the following diagram that shows two membranes connected in series:
Each membrane, as we already know, restricts the flow of water. When the pressure is applied to membrane 1, it stretches and pushes the water to stretch membrane 2. As membrane 1 reaches its limit, it starts to push back against the water pressure that made it stretch in the first place. At this point, membrane 2 may or may not have reached its maximum stretchable potential.
The total pressure applied in the circuit is equal to the sum of pressures across both the membranes. After a few calculations, it has been found out that the inverse of the total capacitance in the electrical circuits where capacitors are in series is the sum of the inverse of individual capacitance. Mathematically, it is written as: 1/C=1/C1+ 1/C 2.
Now if your parents ask both you and your friend to stop playing the games and clean the room, since you will not be jealous of your friend anymore, it will be easier for you to go clean the room, right? (Also, this is fair, isn't it?)
A parallel connection is characterized by all the components connected between the same set of electrically common points, as shown in the following diagram. The current in these circuits is divided, but the voltage across the circuit remains the same. Look at the following two diagrams-you will notice that the positive of the battery and one end of both the resistors share a common point; similarly, the negative of the battery and the other end of resistors share a common point.
The following diagram shows resistors connected in parallel. The total resistance of such a circuit will be determined by the following equation:
1/R = 1/R1+1/R2
Referring back, if the pipe splits into two and each piece of pipe has the same type of sand filter in it, this is what it is going to look like:
Image source: https://ece.uwaterloo.ca/~dwharder/Analogy/Resistors/
This doubles the surface area through which the water is going to flow. Since there is more surface area, the total resistance being offered to water decreases.
The following diagram demonstrates how the capacitors are connected in parallel. The total capacitance of a parallel-connected capacitor circuit is determined by the total sum of the capacitances:
We know both the capacitor membranes are going to stretch and block the flow of water in the individual pipes. Since the total amount of blocking of water is going to increase, we can say that the total capacitance of such a circuit is going to be the sum of individual capacitances. Hence, the equation for calculating the total capacitance will look like this:
C = C1+C2
The combination of series and parallel resistors and capacitors is widely used in special circuits called analog circuits. We will learn more about the implementation of these connections in the following chapters. Let's talk about the water circuit analogy of the same parallel circuit:
Let's now go further and learn about something that is in use for everything in today's world. After reading the following section, you will only be surprised!