# Why There's No Current Flowing in This Part of The Circuit?

One time, in my Physic Class my professor ask us, "How much current is flowing in this circuit?" and everyone answer $$5$$ Ampere (Because, it looks like the resistor is arrange in the series form). But, wrong. My professor said the current flowing in this circuit is $$10$$ Ampere. He said the resistor in the middle isn't affecting the circuit because there's is no current flowing there.

Can anyone explain why there's no current flowing in the middle part of the circuit? (My professor said he would not explain this and I already tried to search on internet but I still could not find the explanation) Is there any other form of electrical circuit that has the same case like this?

note :

Sorry, it's a typo, it should be $$10$$ Ampere. I already edit the question. Thank you for the correction!

• Why wouldn’t he explain it? Isn’t that his job? Commented Apr 14 at 9:04

He said the resistor in the middle isn't affecting the circuit because there's is no current flowing there.

This is correct. There is a wire connected between one end of the rightmost resistor and the other. Therefore there is no voltage across the resistor, and no current through it.

My professor said the current flowing in this circuit is 1 Ampere.

This is wrong. 10 V / 1 ohm is 10 A, not 1 A.

There will be 10 A flowing through the source and trough the upper resistor, and through the wire back to the negative terminal of the source.

it looks like the resistor is arrange in the series form

It does not.

Two components are in series only if they are connected directly together and there is no other path for the current to flow at the junction where they connect.

A wire normally has a small non zero resistance, but we can make the resistance of the bypass wire on the right zero by progressively shortening it until it has zero length and the ends of the middle resistor are joined together as shown in the diagram below:

It obvious the voltage across the resistor is zero so there is no current through the resistor. All the current is flowing around the large loop around the outside so the total current flowing through the circuit is $$V/R = 10/1 = 10$$ Amps.

More formally, the voltage across a section of the circuit is V = IR. If we call the middle resistor R1 and the bypass wire on the right R2, then the total resistance ($$R_P$$) is given by the equation for two parallel resistors such that: $$R_P = \frac{ R1 R2}{R1 + R2}$$ and by setting R2 = 0, the total resistance in that section is zero and therefore so is the voltage across it. With no voltage across R1 there is no current flow through it.

First (assuming this is a typo), there are 10A flowing through the circuit. To answer your question, current will always flow through the path of least resistance. When it reaches the junction after the first resistor, the current could either flow through a resistor of 1 ohm or a wire, which can be thought of ideally as a resistor with 0 ohms (no resistance). Since there is absolutely no resistance in one path, flowing electricity will always go through that path. If current is being split at a junction between two resistors with non-zero values, the current will split up proportionally as defined by the behaviour of parellel circuits.

This is a good video outlining why current behaves that way, using the analogy of flowing water: https://youtu.be/C3gnNpYK3lo?si=u0l1uIPyEfIgvsnd