# Parallel circuit with equal resistance?

If a parallel circuit has 3 paths, all the same resistance will the current divide by 3, and will the voltage throughout all of those paths be the same?

• Yes. ----------- – Olin Lathrop Sep 6 '14 at 19:26
• I'd love to be able to say no but that would be taking your slightly inexact question to extremes. I'm thinking that if the voltage source that produces the current is alternating then you have to consider the inductances of the wires connectingthe 3 parallel resistances. If DC then ditto what Olin said. – Andy aka Sep 6 '14 at 19:38
• Andy: Taken to extremes, if the voltage source is alternating then not only must the inductances be taken into consideration, the mutual inductances must also, as well as the capacitances between the conductors and resistors. – EM Fields Sep 6 '14 at 19:59
• @EMFields Maybe we should say "no" then just to be obstinate (aka accurate)? BTW you need to put a "@" in front of "andy" to automatically inform me. Hell, you probably knew that LOL. Fetch me another drink woman! – Andy aka Sep 6 '14 at 20:56
• @Andy aka: I didn't know that, thanks. Just saying "no" wouldn't be accurate though, would it? – EM Fields Sep 6 '14 at 21:10

If a parallel circuit has 3 paths, all the same resistance will the current divide by 3, and will the voltage throughout all of those paths be the same?

The answer depends on what you mean by 'path' and what you mean by 'voltage throughout'.

But, essentially, the answer is no.

Consider the following circuit: simulate this circuit – Schematic created using CircuitLab

Clearly, this is a parallel circuit and there are three parallel resistances with equal resistance so, in fact, the resistor currents are equal (as is the voltage across).

But the source current is not equal to the resistor currents and, in fact, is -3 times any resistor current.

So, there are 4 current variables associated with this circuit and they are not equal.

If we remove one resistor, there are 3 current variables but the 3 currents are not equal.

The current coming out of V1 will be divided by R1,R2, and R3 evenly. Voltage over each resistor is V1, since that's the potential across by each resistor: they're all hooked up directly to your supply.

Think of it this way: If you hook up voltmeter to R1, you're also measuring across R2 and R3 a the same time, so naturally it's going to measure the same voltage for all three.

The current though, has to split. Current is like water: it takes the path of least resistance, but because all resistors are of equal value, it will split evenly down each parallel branch, thus each branch current will be 1/3 of the current coming out of the supply.

If you want to understand better, I'd suggest reading up on Kirchoff's current and voltage laws: http://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws