We are continuing in 4.2, series voltage sources and we will be looking at series aiding and series opposing. Many electrical circuits have more than one voltage source and these sources may be series aiding or series opposing.

### Series Aiding Voltage Sources

Series aiding voltage sources are sources that are connected so that current in both sources flows in the same direction. If you look at it here we have a power supply and here we have current flowing, negative to positive current is flowing in this direction and the other voltage here, they are both connected so the current flows in the same direction and most of the time if we are using batteries this is the way they are set up. The effective voltage in a series aiding circuit is the sum of series aiding voltages so in this case, we have 15 and five so we have series aiding so we will add up the value. This is much like what you would have if you had a simple flashlight and here you have got the flashing light and the little light bulb here and you have two 1.5volt batteries and this is a 3volt light bulb so you would have series aiding.

#### Series Opposing Voltage Sources

Now here series opposing sources are connected so that sources cause current to flow in opposite directions. Notice this circuit here we have ten volts we have 25 volts and the current notice on this one the current is flowing in this direction on this one the current is flowing this way. In this particular case with reference to ground here we have 25 volts and we have opposing it a minus 10 volts so our net voltage here is 15 volts and that is what we call series opposing.

### Complex Voltage Sources

Then there are complex voltage sources, many circuits involving series aiding and series opposing voltage sources. These types of circuits are referred to as complex voltage sources and the effect of applied voltage is the algebraic sum of the voltage. Notice here the voltage total plus or minus D1, D2 etcetera. Now with this one let us first of all look and see what is opposing and what is aiding, we could look at our batteries here we have 50volts positive polarity here, negative going down here to a positive to a negative to a positive to a negative and if we evaluate we will see that all three of these aids each other so we have 50 + 20 + 10 = 80 volts going in this direction. Then you would notice here we have the positive connected to the positive so this is going to be an opposing voltage. In this case, we would have -75, so our net voltage here would be plus five volts and if we wanted to summarize this, we could say this was 5volts.

Now, there is no ground in this circuit, whether we say this is a positive value or a negative value is somewhat relative because we could have started this circuit out looking at this as a starting point and if we had we would have said well this is 75 and we would have subtracted these, and so then we would have ended up with a minus five volts. Now, in that case, we would have had something that looked kind of like this and we would have said that this was a minus five volts. Now keep in mind we have not talked about this business of negative versus positive voltages and the only difference between the negative and positive is which way is the current flowing. Typically in this one, we would say the current is flowing from negative to positive but since we are saying it is a negative voltage we are going to say the opposite actually the current is flowing from here to here, the opposite.

If we were to change the polarity here, to flip the polarities of our battery and then it would look just like this. Electrically speaking whether we call this minus five volts or whether we show it drawn like as this plus five volts across out T, electrically current is going in the same direction and this is the same as this.

We have taken a quick look at series aiding and series opposing voltages and series circuits so this was our complex voltage source then we showed a series opposing and then we started out with series aiding.