# Simple current flow

Referencing ground circuit simulator(link launches a simulator applet)

Why doesn't current flow in the resistor in the bottom right? What do I need to read about electric theory to be able to correctly trace current flow and solve problems like this?

## 2 Answers

The reason is simple. Current always follows path of least resistance. There is connection to the ground made with no resistor and therefore it will be preferred to one with the resistor.

As for the theory, first make sure that you're familiar with two Kirchoff's laws and with Ohm's law as most of the things are derived from them. After that, you should know that you can short-circuit point of same potential in a circuit and nothing will happen.

Next step is to make an equivalent circuit of the ground points. That is to say that the two grounds are actually shorted together. So this way, you get a current divider. If you do the calculations, you'll get currents which are going through the shorted ground connection (consider it a 0 $\Omega$ resistor for calculation purposes) and the one with the resistor. Numbers will say that the current through the short circuit is infinite and through the resistor is zero.

Another point which needs to be mentioned is the circuit itself. Think about what the word circuit means. A meaning that fits best here is a circular journey or one beginning and ending at the same place;. Current going through the circuit must always move in circles. So in your simulation you have two circles. One is moving from the voltage generator through the left resistor, ground, back up the ground terminal and into the voltage generator. The other is from the generator through the right resistor and back into the generator. It doesn't go through the bottom right resistor because there already is a path back into the generator which has lower resistance.

Also, here is a circuit which is equivalent to your circuit. It is now obvious that the resistor R3 is shorted out.

Once you get the 3 laws I mentioned at the start, go to this article and read it. Make sure you pay extra special attention to the See also section! Theorems listed there are the basic theorems of circuit analysis.

• @Moratinos, think about it, if it were water you have a path but the water is at the same height on both sides. water does not flow because it has equal potential. – Kortuk Mar 25 '11 at 22:40
• Using KVL around the loop after redrawing the circuit solved it for me. Thanks! – user3594 Mar 31 '11 at 18:29

Both sides of the resistor are connected to the same point: ground. Since there is no voltage across the resistor, no current will flow through it.