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.
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1\$\begingroup\$ Welcome! Perhaps this helps? \$\endgroup\$– jonathanjoOct 24, 2022 at 9:24
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12\$\begingroup\$ Which direction were you expecting current to flow in across it? Why? \$\endgroup\$– Joseph Sible-Reinstate MonicaOct 24, 2022 at 18:41
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\$\begingroup\$ By symmetry whatever current flows on the left leg also flows in the right leg so the voltage drops are the same. \$\endgroup\$– copper.hatOct 25, 2022 at 5:00
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2\$\begingroup\$ Trying to explain to us why you think there should be current may trigger the realisation that there won't be 👍 \$\endgroup\$– Lamar LatrellOct 25, 2022 at 5:08
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4 Answers
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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.
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10\$\begingroup\$ 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? \$\endgroup\$– zoghiiOct 24, 2022 at 8:17
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2\$\begingroup\$ Moreover, this particular property of the circuit in question is of importance: en.wikipedia.org/wiki/Wheatstone_bridge \$\endgroup\$– oakadOct 25, 2022 at 5:10
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\$\begingroup\$ 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 ... \$\endgroup\$– mowOct 26, 2022 at 17:52
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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.
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Because there is no voltage across it.
answered Oct 24, 2022 at 8:13
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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.
