circuit analysiscurrentwire
I know that current flows from higher potential towards the lower.
I was wondering why it does not flow towards point "a" and why isn't it divided into "i_y" and "i_x"? And if it happened, it would stuck inside the open wire at point "a", and current "i_y" would head back towards the source. Here, I was thinking, what is the potential of an open circuit in this picture and is it lower enough for the current i to flow in it?
simulate this circuit – Schematic created using CircuitLab
There is nothing "magic" about ground. It is just another route for current to get to its destination.
In most small signal circuits like you have shown the ground symbols are just a way of connecting points together without actually drawing the wires. The ground symbols also act as a reference point against which other voltages can be measured.
For instance, these two circuits are identical:
simulate this circuit – Schematic created using CircuitLab
When you have real earth in there, the circuit is slightly modified to be more like:
The key point is that the current flows from one point of the circuit, through ground, then back into the circuit.
With only one connection to ground there is no circuit for the current to flow through. It can't flow "to" ground, because there is nowhere for it to flow to. There's no difference between ground and a wire dangling in the breeze.
Electricity flowing to ground in high voltage systems has nothing to do with the fact that they're high voltage. It's purely to do with there being a second connection to ground elsewhere in the circuit (usually at the sub-station) which forms the circuit.
You can read more on the different earthing systems on Wikipedia.
why can't electrons also flow from the negative terminal in battery 2, through the right bulb, and into the positive terminal of battery 1?
Because the only way to get to the negative terminal of battery 2 is to come from the body of the battery, and the only way to get there is from the positive terminal of the battery. And the only way to get there is through the switch in the friend's house, which is open so no current can flow through it.
Batteries don't create electrons from nothing. They "pump" them from one terminal to the other via a chemical reaction, causing current to flow (through the battery) from a low potential to a high potential.
Current only flows in complete circuit means the current has to flow through the battery just as much as it has to flow through every other circuit element.
As an aside, it's also why it's silly to say that current always flows from high potential to low --- the battery is a trivial example of when it's the other way around. And it's also silly to say that all current is a flow of electrons in the opposite direction from conventional current --- the battery is a trivial and everyday example of when ionic currents should be considered.
Best Answer
Under steady state conditions there is no place for the current in that branch to flow as others have said. The potential at the end of that wire is equal to the potential at the start of the branch so there's no push. At time zero though there is no potential anywhere except for at the source. When the supply is activated for the first time or a switch closed charge carriers begin to move down the line (we'll use the positive convention for simplicity). At this time the supply has no idea the end of the line is open so it will continue to pump.
As our friendly charge carriers slam into the open circuit they will begin to build up until they are they are strong enough to push back against the flow. Then the system will fall back into equilibrium at which point no more carriers will flow down the open end of the line. The potential will be the same. You could do an experiment with a pulse generator and an oscilloscope and some coax and look at the voltage waveform that appears at the end of the line.
Now depending on the physical structure of the lines and speed of the input signal more interesting things could happen. For instance a high frequency signal might find a coupling path and radiate like an antenna.