# Current without voltage

• B
in a circuit like the one in the attached picture, the voltage between two points in between two resistors should be 0.

But there is current flowing through the circuit.

So what’s going on here? Does ohms law not apply in this situation for some reason?

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jrmichler
Mentor
Add the two points where you are taking measurements to the schematic.

Doc Al
Mentor
Ohm's law still applies. In the idealized case, the connecting wires between the resistors have zero resistance thus essentially zero voltage drop is required to produce a current. In reality, there is some resistance and thus some small voltage drop between two adjacent points on the conducting wires.

vanhees71 and FS98
phinds
Gold Member
One does not normally apply Ohms Law to an ideal wire because you get what I assume is confusing you which is V=IR leading to 0 = I*0 or I = 0/0 and the problem w/ that is that 0/0 is undefined.

vanhees71 and FS98
0/0 is indeterminate.

jbriggs444
Homework Helper
0/0 is indeterminate.
In the context of a limit, 0/0 is an "indeterminate form". That is if one has two functions, f() and g() and if ##\lim_{x \to c}f(x) = 0## and ##\lim_{x \to c}g(x) = 0## then one cannot determine from that information alone whether ##\lim_{x \to c} \frac{f(x)}{g(x)}## exists or, if it does, what value it takes.

As a standalone formula, ##\frac{0}{0}## is simply undefined.

phinds
Gold Member
0/0 is indeterminate.
What's the difference between indeterminate and undefined?

davenn
Mark44
Mentor
What's the difference between indeterminate and undefined?
"Indeterminate" is used in the context of limits, as @jbriggs444 already said, and means that some work is required to determine whether they represent numbers. Some indeterminate forms are ##[\frac 0 0]##, ##[\frac \infty \infty]##, ##[\infty - \infty]##, and ##[1^\infty]##. Most textbooks write these forms in brackets to emphasize that they are "forms" rather than actual numbers.
The following limits are examples of the first three types I listed:
##\lim_{x \to 1}\frac{x^2 - 1}{x - 1}##
##\lim_{t \to \infty}\frac{t^2 + 2}{t^3 - 1}##
##\lim_{y \to \infty}y^2 - y^3##
These are called indeterminate forms because it's not obvious at first glance that they represent a number. By taking a limit and subsequent algebraic or other operations, one can determine that a limit actually exists or not.

As for undefined -- the division of any number by zero is undefined, as is taking the square root (or fourth root or any even root) of a negative number is undefined (if we're dealing with the real-valued square root function). In general, attempting to evaluate a function at a number not in its domain is undefined.

davenn and phinds