Sometimes texts tell us "that" something is so-and-so, but not "why." For example, total resistence in a series circuit is the sum of the resistences. Or, total resistence of a parallel circuit is less than the smallest resistence. This tells us "that" but not "why."

The series circuit is intuitively easy to understand. You have resistences, one after the other, they add up -- makes immediate sense. You don't have to really get into the "why" on this one.

But the parallel circuit is different, at least to me and some others I've talked with. Somehow, it's not immediately apparent that the "total" resistence is less than the lowest resistence, i.e., the lowest resistor in the circuit. Obviously, using the "water pipe" analogy gives an immediate, intuitive understanding that the total resistence of a parallel circuit is less than the sum of the resistences/resistors. But that the total resistence is less than the smallest resistor -- that comes as a surprise. The question is "why" is this true. How do you conceptualize this for the student? Here's my take.

Let's take a circuit with three resistors, 10, 20, 30 ohms. When the current moves into the circuit it splits up and proceeds to move across each resistor at a certain speed depending on the amount of resistence encountered, the pressure (voltage) being the same for all. They move across the lowest resistor at the fastest rate among the three resistors. The elctrons move across the 20 and 30 ohm resistors at a slower rate, but some do go across.

Now to conceptualize it, a certain number of electrons go across the 10-ohm resistor in a certain amount of time. With a predetermined amount of pressure (voltage) and the resistence/resistor remaining the same, the number of electrons going across the resistor is set and cannot in these circumstances change. Thus if the circuit only had this one resistor, the number of electrons getting to the other side would be the same. In other words, the rest of the circuit is irrelevant if we just focus on this one "electron bridge." Now, in the parallel circuit, while these electrons are moving their merry way across the 10-ohm resistor at a speed/amount determined by the pressure (voltage) and the resistence in the resistor, other electrons are not just waiting in line, they are going over the other two resistors, albeit at a slower pace.

Thus, in a certain period of time, the electrons moving across the 10-onm resistor are joined on the other side by electrons that have gone through the 20 and 30-ohm resistor "bridges", even if they have gone over at a slower rate because the resistence was higher. So, overall, there are more electrons that make it over the various bridges in a certain amount of time than get over just the one "bridge" of the 10-ohm resistor. So, overall, there is lower resistence in the circuit, because more electrons get to the other side of the circuit that those just going across the 10-ohm resistor/bridge.

Long-winded, but this "why" the overal resistence of resistors in parallel is less than the resistence of the lowest resistor.