# Why is the resistance of parallel circuits lower than either of the individual parts

I am watching this tutorial, and topic of parallel circuits came up. In the below image, the combined resistance is 60Ω, which is less than either of its parts (150Ω and 100Ω).

I understand how the combined resistance is calculated, with the 1/(1/150Ω + 1/100Ω) formula, but I still don't understand why the overall resistance is lower. Wouldn't it be impossible for anything to move through with less than 100Ω resistance?

My understand is that the electrons want to get from positive end of the voltage source to the negative end, and resistors reduce the speed that can happen. So, why does adding two resistors in parallel offer less resistance than if there were only one?

• Water/air flows more easily in two pipes side by side than just one since it is equivalent to a single pipe of a larger diameter. Not a perfect analog, especially for series pipes and series resistors, but thinking about speed of electrons tends to mess people up. If you insist of thinking about speed, then you can say the 150 ohm resistor causes things to slow down and the backlog finds its way through the 100Ohm instead. And since the 100Ohm is actually easier to get through, more electrons end up going that route for more current. But thinking about speed will still tend to mess you up. Apr 5, 2021 at 3:28
• @DKNguyen Using the water/pipe analogy, I think that the length and width of the pipe would both matter ... but I guess both those attributes are sort of combined here in the term "resistance" Apr 5, 2021 at 3:29
• @maxpleaner The length and width do matter! That's how you make resistors of different resistances (for most types at least; carbon composition resistors are weird)--they contain a resistive element that's cut to a specific length and width for each resistance value they want to manufacture. Apr 5, 2021 at 15:44

The current through the 150 Ohm resistor will be 0.2 Amp, whether the 100 Ohm resistor is there or not, and the current through the 100 Ohm resistor will be 0.3 Amp, with or without the 150 Ohm resistor.

With both resistors present, the total current will be 0.5 Amp. To get that current with a single resistor, you would need a 60 Ohm resistor, by Ohm's Law.

• I am still a bit confused as to why the current is the same for each of the parallel resistors ... is there another explanation beyond just "that is just what the measurements show us to be true"? Apr 5, 2021 at 3:39
• The current is not the same in each resistor. The current in either resistor is determined by its resistance and the supply voltage, independent of any other current paths. Another anology - two roads from A to B can move twice as many cars as one road. Likewise, multiple possible current paths can move more current than a single path of the same resistance. Apr 5, 2021 at 3:45
• I think what trips me up is thinking that without the resistors, the current would be infinite ... that's the only way I can really conceptualize it ... the traffic analogy is difficult, because in a real life traffic jam that lasts a mile long, a one-block detour is not going to increase the traffic speed much .. but I guess that just means the detour has a very high resistance Apr 5, 2021 at 4:04
• " the total current will be 0.5 Ohms" should read " the total current will be 0.5 A". Apr 5, 2021 at 5:33

Mechanical analogy: Resistors are like pipes. Resistance rather than being a measure of how big a pipe is, describes how small it is. If you have very narrow pipes (higher resistance), you get less water through. If you have longer pipes, you lose energy getting water through depending on how fast it flows. If it doesn't flow at all, you can transfer a lot of pressure and apply force over that area without losses, but force is only part of energy - you need to move a distance (flow some volume) to actually transfer energy. (Voltage is pressure and current is flow)

If you have two narrow pipes in parallel, you can move double the water. But if you stick them in series, it's like having one long pipe.

Bonus: everything is a pipe- just the holes are sometimes very tiny to the point where the amount that flows is basically 0. It might even be better to think of it all as mud with various levels of porosity instead of pipes.

My understand is that the electrons want to get from positive end of the voltage source to the negative end, and resistors reduce the speed that can happen.

While in a metal resistance does reduce the speed of electrons, this is not important to understanding parallel resistance. Instead, resistors reduce how much current can flow for a given voltage. Putting two resistors in parallel doesn't necessarily increase the speed at which charges move, it increases the number that can move at once. If you put two equal resistors in parallel, you let twice as much current flow and therefore you reduce the resistance to one half.

• The current in a is defined as the electrical charge passing the cross section of a conductor in the unit of time (s). With zero current there is no (averaged) movement of charge carriers (electrons). With increasing current more electrons pass a given cross section of the conductor. As the number of free electrons available is constant this is possible only if the resulting average speed of the electrons increases. Conclusion: The averaged velocity of the electrons is proportional to the current. Apr 5, 2021 at 5:51
• @Elec1 Good point. I should have said that the velocity of the electrons is not relevant to understanding resistance in a parallel circuit (since the electron velocity may increase or decrease as you put more elements in parallel). Apr 5, 2021 at 13:55