# Why does current remain same in a series circuit?

Current is the rate of flow of charges with time. When passing through each resistance in a series circuit, charges lose energy and "slow" down due to collisions with atoms (metal cations). When time increases, current decreases. I agree number of charges remains same but what about time?

• Current doesn't decrease with time. Current decreases when the potential difference driving that current decreases. Individual electrons accelerate and stop when hitting atoms in the conductor, but current represents the sum total of all electrons moving through a conductor. Mar 18 '19 at 22:03

## 2 Answers

Imagine a scenario. Take a battery having a potential of $$V$$. The ends of the battery is connected by a wire that is resistance less(an ideal approximation). In that case, the electrons in the wire are offered no 'resistance' and hence, they are free to move from the negative end to the positive end of the battery. From simple application of Ohm's law $$I=\frac{V}{R}$$ we see that the current is not defined, but in the limiting case of $$R\rightarrow 0$$, $$I\rightarrow \infty$$. Though the Ohm's law is an approximate law and we need a better treatment of the scenario to understand what is happening, we as of now know that the electrons don't travel through the resistance less wire instantaneously. There are electrons all along in the wire which just 'drift' towards the positive end of the battery without any obstruction and so quite fast(not instantaneously).

Now, if we include a resistor of resistance $$R$$ in this scenario, the drift of the electrons are no doubt restricted and this restriction of the motion of charges through the resister is indeed what causes the potential drop across the resistor, and the drift through the resistor occurs at a smaller rate, hence the smaller current.

For two resistors in series, this drift is slowed by both of the resistors(hence lesser current as compared to the single resistor case). However, the drift velocity through the entire wire has to remain the same as electrons can't accumulate anywhere in the wire if there are non regular speeds of their drifts as pointed out by @Nuclear Wang and the OP wrote in the comments. Also, electrons do lose energy due to collisions and that loss appears as heat that reduces the potential in due time and hence the current all in all deceases. But the current can't have various values in such a series circuit.

• Thanks alot ! That's great explanation. I just have this query in mind that whether electrons are "accelerated" in moving through a circuit or whether they move with uniform "drift" velocity? Does resistance slow down charge carriers so that instead of accelerating, they move with uniform drift velocity? Mar 19 '19 at 17:10
• The electrons do accelerate from rest when a potential is applied, however they repeatedly collide with lattice atoms and loose energy. Hence, in a crude sense, we take up that the elecrtons move at a constant drift velocity (which is in fact an approximation) given the applied potential $V$ and the resistance $R$. Mar 19 '19 at 19:21

If the current in a series circuit diminished with each resistive device, you'd wind up with a pileup of electrons further down the circuit. If the circuit had a 10A flow at the start of the circuit and a 1A flow at the end, you'd have 10C worth of electrons arriving somewhere and only 1C worth leaving - you'd have 9C worth of electrons piling up somewhere every second! Complete circuits do not spontaneously accumulate charge somewhere in the circuit.

You can think of it like a garden hose - water entering one end will come out the other end at the same rate, otherwise something is very wrong with your hose.

• Electrons won't accumulate because they'd repel the incoming electrons. Battery would have to do more work to push them, that's resistance. With increased resistance, current decreases. Mar 18 '19 at 18:59
• @ShahzebCheema You're correct, electrons don't accumulate, because the current is determined by the resistance of the entire series circuit. I think you just answered your own question - if electrons did accumulate, it would slow the upstream flow of electrons until it matched the downstream flow of electrons (the battery can't push any harder than it already is). Hence, current is identical everywhere in a series circuit. Mar 18 '19 at 19:12
• Indeed that's true. Thanks alot... Mar 19 '19 at 17:12