Why electrons flow through a wire connected to a battery? I would like to know why does electrons flow through a wire connected to a battery as said in AC/DC: What's the Difference?.It tells that "the electrons that are stripped from the carbon electrode is collected on the zinc can" and then tells

The electrons at the negative terminal want to go to positive terminal, they just need a way to get there. In our light bulb circuit, the way to get there is through the wire.

Why couldn't the electrons go to the positive terminal through the electrolyte(potassium hydroxide) instead of going through the wire?
 A: Batteries use a type of reaction called a redox reaction that involves the transport of electrons. Rather then the carbon zinc battery, which is a bit complicated consider the simpler example of a zinc copper battery as taught in school science lessons across the world. The reaction is:
$$ Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu $$
So the reaction dissolves the zinc electrode and produces copper metal at the copper electrode. The reaction goes this way because the overall free energy of the Zn/Cu system is reduced in doing so.
If we look more closely the reaction involves three steps:


*

*$Zn \rightarrow Zn^{2+} + 2e$

*transport of the electrons to the copper

*$Cu^{2+} + 2e \rightarrow Cu$
So as the reaction goes electrons flow from the zinc through the battery to the copper. In effect the reaction acts as an electron pump that pumps electrons from the zinc end to the copper end. So if you connect an external wire from the copper to the zinc the electrons flow out of the copper, through the wire and back to the zinc, then complete the loop by flowing from the zinc to the copper inside the battery. Electrons flow in that direction because the chemical reaction forces them to.
The traditional zinc-carbon battery uses a reaction between zinc and manganese - the carbon is actually just an electrode and doesn't take part in the reaction. While the reaction is more complicated the basic principle is the same. The zinc reacts to form $Zn^{2+}$ and electrons and the manganese absorbs the electrons. So just like the zinc-copper battery the electron flow is driven by the chemical reaction.
A: Via a series of chemical reactions a battery sets up a surplus of electrons on the zinc (negative) plate and a deficit of electrons (positive charges) on the carbon (positive) plate because it is energetically favourable to do that.
You can think of the reaction as a zinc atom producing a zinc ion and two electrons with the release of energy.
Assume that the battery is not connected to an external circuit.
The chemical reaction is in effect forcing electrons to move from the positive carbon to the negative zinc.
The build up of charge on the carbon and zinc will continue until the electric field due to the charges on the zinc and carbon is such that the chemical reaction cannot move any more electrons from the positive carbon to the negative zinc.
This occurs when the potential difference across the terminal of the battery is about 1.5 volts.
The battery is like a pump taking electrons from the carbon electrode and depositing them on the zinc electrode, but like a water pump which can only pump water to a finite height the same is true of the electron pump which can only move electrons across a finite potential difference.  About 1.5 volts in the case of a carbon-zinc battery.
Now when a external conducting path is added between the carbon electrode and the zinc electrode, electrons will flow from the zinc plate through the external conducting path to the carbon electrode.
Whilst this is happening the chemical reaction (electron pump) with move electrons inside the battery from the positive carbon electrode to the negative zinc electrode to maintain a potential difference of 1.5 V across the electrodes.
So the answer to your question is that it is not energetically favourable to move electrons from the zinc plate to the carbon plate.
The electrical circuit has electrons continuously flowing around it.  Electrical energy comes from chemical energy in the battery and if the external circuit is a resistor then heat is produced from the electrical energy.
A: Actually the flow of electrons is not that cause the light to glow. The electrons are just carriers of energy. I will make it clear. Consider a bulb connected to a battery. The wire is a conductive metal which means that it is in solid state. So the inter atomic spaces is very less. So the electrons can't move that much freely. There arises a no. of collisions with the atoms in the lattice. These collisions causes the electrons to lose their energy (since the collision is inelastic) and hence the kinetic energy of electron appears as lattice heat.
So the velocity of electrons get averaged. Theoretically, when a charge like an electron is placed in an electric field, it should accelerate. But the velocity of electron is averaged inside the wire. So if you switch on the current, the electron from the battery takes some sufficient time to get to the bulb. But that's not what happens in real life. The bulb glows instantly when you switch on. Then, that means it is not the flow of electrons that make the bulb glow. The explanation is like this. 
Consider an electron close to the battery. It absorbs electrical energy from it and hence moves. When it reaches in the vicinity of neighboring electron, there arises electrical repulsion between both. So one would expect that both will fly apart. But the first electron cannot go back as there is continuous energy from that direction. So the configuration holds some potential energy. Thus the neighboring electron starts to move. this happens through the entire wire. Even though electrons can move only at some average velocity, due to repulsion the effect of electrical energy get transferred instantaneously through the wire.
Now at the bulb, the bulb has some resistance. So the electron loses energy there which is picked by the bulb and convert it into light and heat energy.
There is no conduction possible through the internal arrangement of a battery because the two electrodes are separated by each other.
