Yes, the downward pointing arrow typically denotes a negative voltage, as this example is showing...From my understanding, all grounded nodes are connected to each other. Can the same thing be said for all the black triangles that are -5.7 volts in the picture?
This probably needs to be qualified somewhat. For instance, the inputs of an opamp in the active region are generally considered to be equipotential. But, even from an analysis standpoint, they can't be strapped together because current cannot flow from one to the other.In basic circuit analysis, equipotential nodes can be strapped together.
If they are actually equal voltage (and will stay the same), nothing bad can possibly happen.... but if they do not stay the same voltage for whatever reason, it might. Two nodes of the same voltage can not cause a current flow across them... if any current flows, one is not the same voltage as the other.But two separate nodes at the same voltage does not necessarily mean they are (or should be connected as) the same node. If one was the circuit supply 5V power and the other was a stable 5V reference voltage then you would not want to tie them together as bad things would likely happen.
What I said is absolutely correct. Two equipotential voltage nodes can be analyzed as the same nodes strapped together. Op amp inputs are not because in nearly all operation modes, they will not be the same voltage:This probably needs to be qualified somewhat. For instance, the inputs of an opamp in the active region are generally considered to be equipotential. But, even from an analysis standpoint, they can't be strapped together because current cannot flow from one to the other.
Then they are not equipotential if current flows from one to the other, since any current flow can only occur with some electromotive force (voltage) driving it.This probably needs to be qualified somewhat. For instance, the inputs of an opamp in the active region are generally considered to be equipotential. But, even from an analysis standpoint, they can't be strapped together because current cannot flow from one to the other.
Not true. The simplest example is a superconducing magnet in persistence mode.Then they are not equipotential if current flows from one to the other, since any current flow can only occur with some electromotive force (voltage) driving it.
You can always connect two points of equipotential with no change. If there is a change, by definition, that proves they were NOT equipotential or were not equipotential under all ccircumstances.Equipotential or isopotential in mathematics and physics refers to a region in space where every point in it is at the same potential
Electrical conductors offer an intuitive example. If a and b are any two points within or at the surface of a given conductor, and given there is no flow of charge being exchanged between the two points, then the potential difference is zero between the two points.