# Why does the resistor connected in parallel in the middle not get any current? The horizontal resistor in the middle does not get any current and it is also ignored when calculating the total circuit resistance which is:

[(1/(1+1))^-1 + (1/(1+1))^-1]^-1 = 1 kΩ

I don't understand why it gets 0 current.

• Welcome! Perhaps this helps? Oct 24, 2022 at 9:24
• Which direction were you expecting current to flow in across it? Why? Oct 24, 2022 at 18:41
• By symmetry whatever current flows on the left leg also flows in the right leg so the voltage drops are the same. Oct 25, 2022 at 5:00
• Trying to explain to us why you think there should be current may trigger the realisation that there won't be 👍 Oct 25, 2022 at 5:08

Both ends of the resistor have identical voltage. As there is no voltage difference over a resistor there will be no current through it. It can be seen from Ohm's law.

• so if the 2 vertical resistors on the top would have different resistances, there would be a voltage difference across the horizontal resistor giving it a current? Oct 24, 2022 at 8:17
• That's correct yes Oct 24, 2022 at 8:19
• Moreover, this particular property of the circuit in question is of importance: en.wikipedia.org/wiki/Wheatstone_bridge Oct 25, 2022 at 5:10
• In practice, you'll have a tiny current because the resistors will never be exactly balanced. Not much of a problem here with the high resistances, but something to keep in mind when you connect potentials that are supposed to be ground ...
– mow
Oct 26, 2022 at 17:52

This circuit involves a concept called the Wheatstone Bridge. You can read more about it here.

Basically, if $$\frac{R1}{R2} = \frac{R3}{R4}$$, the potential at points A and B will be equal. For current to flow, there must be some potential difference to drive it. However, since there is no potential difference between the points A and B, no current can flow between them. Hence, the resistor placed between the two points can be ignored. Because there is no voltage across it.

current only flows when there's a potential difference (PD) across the element. If both ends of the element are at the same voltage, then no PD, therefore no current.