# Series Circuits (part 1)

#### Circuits

At the beginning of chapter four, we mentioned that we were going to be looking at four basic ways that circuits are constructed and the first method we are going to be looking at and the most basic is series circuits.

As a technician, it is important to understand series circuits. A series circuit is characterised as having only a single path for current flow and so here we have a source of EMF and we have a component connected as down here we have a voltage source and a component connected in this case a light bulb but in both these cases there is only one path for current flow. There is only one way that current can flow, there are no alternative paths there is only one path and that makes this a series circuit.

Series components are connected such that only a single path exists for current flow without encountering any branches in the circuit.

### Series Circuits

If every electron that leaves the negative terminal of the power source has only one path for current then the circuit is a series circuit and so you see in this case here the negative side of this… and the positive… every electron that passes only has one path for current and so we will call that a series circuit. In a series circuit as there is only one path for current flow, each component has the same current flowing through it as flows through the entire circuit. That is an important aspect of series circuit. Since there is only one path for current flow then it is the same current that goes through R2, R3, and R1, it is the same amount. It is kind of how like when we talked about that hydraulic system and how the hydraulic system has a pump and if it is a loop the same amount of fluid that goes through this goes through this and that was the analogy to the hydraulic pump that we talked about in previous lessons.

Now, this particular circuit here I have a question on the above series circuits… well, this is obviously a series circuit… in this case, we start out with our voltage source, current comes in and goes through all… the current from the source goes from R2, but now we have what we are calling a branching and this is going to be a parallel circuit, so the circuit is going to go through this branch of resistors here and then come back through this circuit. This is no longer a truly series circuit. It is a series circuit but it has a parallel branch over here and later in this chapter we will be looking at parallel circuits.

### Intuitive Relationships

Series circuits, this is a section called intuitive relationships and intuitive relationships are things that just kind of make sense and in series circuits there are some things that are just intuitive about a series circuit and you text will give a little bit of a discussion about each one of these if it is not clear as I got over it. First one, all currents are equal in a series circuit, all current through this particular circuit will be equal. The total resistance is greater than any one resistance. Maybe that is obvious but the total resistance of all the components is going to be greater than any one resistance. Likewise, the total power is greater than any one component dissipation so the total power dissipation of this circuit is going to be greater than any single component. Larger resistance drops have higher voltage drops. That may not be so obvious but if we remember that voltages… remember we talked about what is voltage in terms of Ohms law? We said that voltage equals I times R, now remember that we have the same current flowing through this entire circuit so we say the current is going to be we will just show a flat arrow showing horizontal, the flat relation doesn't change. If the resistance goes up then the voltage drop across that component will increase and so we have three components here, this is the largest 30k so this would have the largest voltage drop based upon the formula that current times resistance equals voltage and in since this has the largest resistance and all current are equal the drop here will be the largest.

Finally the last intuitive relationship, total voltage is greater than any one component voltage, so the total voltage, in this case, is 120volts and this will be greater than the drop across any single voltage and those are referred to as intuitive relationships about series circuits.

### Mathematical Relationships

Mathematical relationships, in a series circuit the following relationship exist with regard to current voltage and resistance. The first one, we have something here call IA, in this case, A has to do with applied current, the current that comes out of our power supply is equal to that which goes through R1, R2 and R3 and mathematically that is what that states. Resistance, the RT, in this case, is the total resistance. The total resistance of all components, in this case, is going to equal R1 + R2 +R3. Then we have VT for voltage and again this is total voltage in this case 120volts but it will equal the voltage drop across R1, R2, and R3. The applied voltage in a closed loop is equal to the sum of the component voltage drops. This important relationship is known as Kirchhoff's voltage law.

### Polarity of Voltage Drops

When current flows through a resistor there is a corresponding voltage drop across that resistor. The point where a current enters a resistor is negative and the end where the current exits will be positive. So here we have our power supply, it is supplying current, the current is flowing in this direction and notice we are on the negative terminal here, but the first point here where we enter a component the polarity is going to be negative and then the other side will be positive. When we do our circuit simulations you will be able to go in with a volt meter to measure this and confirm that is in fact true. The polarity here would be minus to positive, minus to positive, minus to positive. It kind of makes sense if you think that you had a battery and you had just a single component, this component over here and the battery is positive to negative, that the polarity across the component would be just like that; the positive would be at the positive side the negative at the negative side. At any rate, the point where current enters the component is going to be the negative side of the component.

### Closed-Loop Equations

The following procedure can be used to produce a closed loop equation in to describe a series circuit. There are two steps in this. First one, label the polarity of voltage drops and sources, so here we have got polarity, we did this previously okay, positive to minus and then minus to positive minus to positive minus to positive. Start in any point in the circuit and write the voltages indicating polarity as you progress around the loop in either direction. Remember the polarity of the voltage drop is determined by the direction of current flow. Finally, move around the loop and write the voltages that are on the exit ends of the components.

### Kirchhoff's Voltage Law

We can do this… let us go to the next slide; there is a little more space on the next slide. What we are actually doing is applying Kirchhoff's voltage law and another way to state this law is that the algebraic sum of all the voltage drops and all the voltage sources in any closed loop equals zero. You can do this by summing the polarity of each component based on where this current enters the components. We look at this and we think well current is flowing in this direction and we are going to evaluate the polarity based on where does current enter that specific component. Let us start at this point here. The polarity where a current enters the power supply is positive so we start out with 120, and then we are going to sum based on where does current enter the component. We start here with a positive, then we are entering this component and we have a minus sign so we go -60 and continue around to -40 continue around to -20. If we sum these values the sum is going to be zero. That is what we were alluding to in the previous slide, that the sum of all voltages around a circle are going to equal zero and that is another way of stating Kirchhoff's law. If you were a conventional person and you wanted to do it going the other direction you could just as well do that but you must be consistent if you are going to do this. If we say that positive forces are moving in this direction then we would start out at this point and we would start out with -120 going this way, + 20, +40 and then +60 but again out sum would be zero.

Now I am going to encourage you to read the text on this particular subject and there are several circuit simulations that you can do in multisim to approve this and you need to be able to go into the simulation and attach a multimeter and actually measure these drops and see for yourself that this is the way it is and Kirchhoff's voltage law does make sense. If you algebraic sum all the values in a series circuit the sum will be zero.

We have looked at Kirchhoff's voltage law here in solving a closed loop equation, we have looked at polarity and voltage drops, we have looked at mathematical relationships, we looked at some intuitive relationships of series circuits and we looked at what is a series circuit and what is not a series circuit. This concludes our section on series circuits.