# Why the current entering and leaving the battery in an electric circuit needs to be same?

When somebody applies Kirchhoff Laws to the circuit consisting more than two batteries, the current leaving the battery is as same as entering the battery.

I have no problem understanding the circuit consisting of only one battery due to charge conservation. But if there are more than one battery, the current entering and leaving the battery doesn't need to be same. Total charge could be divided in a such way that more charge ends up in one, less charge in other. But the total charge could be conserved again. For example, the image applies Kirchhoff law in which the leaving and entering current for each battery is the same.

One example here:

http://www.physicsandmathstutor.com/a-level-physics/finding-current-circuit-using-kirchhoffs-laws/

• Oh yes it does! – Andy aka Feb 7 '18 at 19:07

There's the usual, droll electronic laws answer. But I'll take a different perspective that I think gets the point across more deeply.

Take a capacitor. You know that it can store charge, right?

So, given your thinking process, you might then imagine that the current on one of the terminals can be different from the current at the other terminal of the capacitor. And you might ask, why must it always be that the current goes through the capacitor instead of having current X leaving the left terminal of the capacitor and current Y entering the right terminal of the capacitor, where $X \ne Y$. Right? I mean, you would think this could possibly happen?

Not usually. Just possibly?

Or, perhaps, that we might set up two capacitors in series (like your batteries) and where you would imagine that one of them could have a different current in it than the other one. One could "build up charge" so to speak, you might argue.

Yes?

No.

Sometimes, it is very hard for people to realize this. But the force acting between two charges is huge. Not just big. Not humongous. But unimaginably huge. The effect is that matter in nature is essentially neutral. At all times. Ionization does occur. But it is ever only for very small numbers of charges.

Let's take your two batteries. They are separated, let's say, by a distance of $10\:\text{cm}$. They are each $10\:\text{cm}$ wide, too. So the mean distance between their centers is $20\:\text{cm}$. Let's say that the current leaving and entering one of these batteries is $1\:\text{A}$ and the current leaving and entering the other one (in series, as you say) is $2\:\text{A}$. Then it must be the case that a charge differential is building up between them, based up the missing $1\:\text{A}$ that is accumulating into one of these batteries.

(Keep in mind we are assuming magic batteries here that can actually manage to keep and hold a lot of charge.)

How long might you wait until the force acting between these two batteries is 2000 lbs, or one ton!! Well, it's $20\:\text{cm}\cdot\sqrt{\frac{8900\:\text{N}}{k_e}}\approx 200\:\mu\text{C}$. At the differential rate of $1\:\text{A}$, this would take about $200\:\mu\text{s}$. In that short time, assuming magic batteries here, you'd already have an incredible force acting between those batteries.

In reality, that of course does not happen.

There can be moments when things are not exactly in balance. But these are for very short moments while charges redistribute.

The universe needs pretty much everything in it to be relatively neutral.

Gravity on the other hand is pathetically weak. You can accumulate a lot of mass before any serious force occurs. But with electric charges?? WoW! No way. Everything stays pretty much neutral pretty much all the time.

At least, on Earth.

So why do all the currents summing into a node have to equal all the currents exiting the same node?? Because if that didn't happen, it would take no time at all for the circuit to be literally attracting nearby planets towards us.. or perhaps repelling the Earth from the sun at a fast pace.

It would be cool, I suppose. That kind of power would be nifty to possess. Rocket ships would be trivial to launch. Just turn on the current for a little bit and whoosh!! Up into space they'd go.

Life would be so much different.

But then we'd probably not be here, either.

• This is actually a really great answer, in that it shows that the difference between conventional current and electrostatics isn't fundamental physics but one of quantity, to several orders of magnitude. – pjc50 Feb 8 '18 at 10:35

Think of multiple water pumps in some complicated plumbing system. For each pump, the water going in and coming out are the same. If it weren't the water would have to either build up in the pump, or the pump would have to magically create water.

Batteries are pumps for charge. A battery adds energy to the charge flowing thru it, but it doesn't store nor magically create charges.

Another way to look at this is that each battery is eventually in only one loop of the circuit. The same current flows thru all parts of that loop section. The wire immediately connected to one end of the battery has the same current going in one end as there is coming out the other end too.

The Law of conservation of charges applies to each voltage source in your circuit. Current is rate of change of charges. Since battery doesn't store any charge, the net charge should be zero. So the amount of charges flowing in per second into the battery, should be equal to the amount of charges flowing out of the battery.

If more current (electrons) leave a battery than enter it a positive charge will build up and stop the current flow. The reverse is also true. It applies to all circuits.