Electronic – Circuit and condition

Perhaps a worked example would make things clearer.

Suppose I had three lamps - each has a different working voltage and takes a different current. What would happen if I connected all three in series and connected them to a 9V battery.

For the purposes of illustration only (keeping it simple) I am assuming the lamps work as pure resistances that don't change their values.

First we calculate the individual resistances of the lamps. In this case 6,24 and 15 ohms.

The total circuit resistance will be 6 + 24 + 15 = 45 ohms

The current that will flow around the circuit will be

                               9/45  = 0.2 Amps

This is much less than any of the rated values because there is MORE resistance in the circuit

Each lamp will 'drop' a different voltage

lamp1 will drop 0.2 x 6 = 1.2V

lamp2 will drop 0.2 x 24 = 4.8V

lamp3 will drop 0.2 x 15 = 3.0V

If we add up all the voltage drops we get 1.2 + 4.8 + 3.0 = 9V

In other words the sum of the voltage drops around the circuit is equal to the supply voltage (kirchoff's voltage rule)

Again note that these voltages are not related to the ratings of the devices.

That's simple: in high school they did not tell you the bad part of the story: Y-\$\Delta\$ transform.

The series parallel technique works well... Almost in all cases, but when you need to solve such a bad guy then you need to use all your weapons. You should read the wikipedia article, anyway given a three impedances circuit, either arranged as a star, i.e. a central node common only to the impedances and three external nodes, or as a triangle, i.e. three nodes where only two of the tree impedances connects, it is possible to transform it in the other fashion, that is transform a triangle in a star and vice versa. The formulas are all written on wikipedia, I am not copying them here, the interesting part is that with series, parallel and Y-\$\Delta\$ transforms you can solve almost any network.

In your particular case you'd trasform the ABD triangle in a star with tips in ABD and center c (that's a new node), then compute the series cA->AC and cD->DC and then the series Bc->cC. If you write it down you'll grasp this in seconds.

There also is another transform called star-mesh transform, which is a generalization of the Y-\$\Delta\$ transform. Please note that with more than three impedances, that is our case of interest, the transform is not reversible since it results in an increased number of impedances.