# Parallel and Series Circuits Question (Electron Flow)

So this is a pretty basic question, I understand the aspects of parallel and series circuits but don't understand why?

For instance:

1. How can the Battery be "drained" faster when say 3 LEDS are connected in Parallel.....How does the battery "know" I suppose? And why is this any different than a Series Circuit?

2. In a Series Circuit if we had an LED connected in between a 5v Battery such as +----LED----(Ground) We'd experience a voltage drop of 5v over the LED, however 2 leds would just be 2.5 voltage drop a piece.....I don't understand WHY that is? Shouldn't all the "Pressure" from the batterys voltage be used after the first LED? Furthermore how can equal pressure/voltage get distributed in a parallel circuit.....it just confuses me at "why".

I know this kinda stuff I don't "Need" to know the physics of it....I just "have" to know this stuff otherwise Im not satisfied with how it works haha.

• – Phil Frost Feb 23 '13 at 13:09 (Public domain image from Wikimedia)

What the load line graph shows is two equations that need to be solved to get the operating point of the circuit. I is the current going around the circuit in the clockwise direction. VD is the potential as indicated in the schematic. The diode response curve shows all the possible combinations of I and VD that are consistent with the diode's characteristic equation:

$I(V_D) = I_s(\exp{(nV_D/V_T)}-1)$.

And the load line curve shows all the possible combinations of I and VD that are consistent with the characteristics of the Thevenin source formed by the battery and the resistor:

$I(V_D) = (V_{DD} - V_D)/R$

Since there's only one combination of I and VD that satisfies both equations, shown by the intersection of the two curves, that will be the operating point of the circuit.

When you put two components in parallel, their voltage is the same and their currents add, so the response curve of the parallel combination stretches in the "I" direction. When you put two components in series, their current is the same and their voltages add, so the response curve of the series combination stretches in the "V" direction.

if we had an LED connected in between a 5v Battery such as +----LED----(Ground) We'd experience a voltage drop of 5v over the LED,

This isn't a realistic scenario, because of the steep shape of a diode's response curve. If you put 5 V across a diode you would be more likely to blow up the diode than have a working circuit.

That said, real voltage sources like batteries have some parasitic series resistance (and real diodes also have some parasitic series resistance), so if you had a beefy enough diode, you could find its operating point when powered by a 5 V battery using a load-line analysis like the one shown in the picture above.

however 2 leds would just be 2.5 voltage drop a piece.....I don't understand WHY that is? Shouldn't all the "Pressure" from the battery's voltage be used after the first LED?

If you have two devices in series, their current is the same. If they're identical components (with identical response curves), that means the voltage across each one has to be the same as the other one. So if you put 5 V across a series combination of identical parts, you know you'll get 2.5 V across each of them.

Furthermore how can equal pressure/voltage get distributed in a parallel circuit

In a real circuit it's not perfectly distributed because there's some resistance in the wires connecting the parts. But in a model with ideal wires, it's the definition of the wire that the voltage is the same at all points on the wire. And this approximation is good enough for analyzing the vast majority of circuits.

1) How can a bathtub/sink/bucket be 'drained' faster if there are three hoses instead of one?

2) When you put three springs end-to-end and stretch (or compress) them, are all the springs compressed (streathed) or only the one at one end?

Power drains out of a battery like water drains out of a bucket. Gravity makes the water go: electrochemical potential makes the electrons go. If you put more holes, or make the holes bigger, the water is gone sooner. If you put more resistors, or make the resistors more conductive, the power is gone sooner.

The resistors in series act like springs in series because the are both LINEAR systems. That word, LINEAR, means exactly that when you put them in series, the pressure is shared between them. Just like saying a spring, or a resistor is RED, or BLUE, some materials are LINEAR - the pressure is shared along the length. Resistors are manufactured out of material like this because we WANT them to share like that. If we didn't want that, we would use some other material.

How do they 'know' to share the load? They don't know. They bounce around until the load is shared. For resistors, the 'bouncing' is very fast -- at the effective spead of light -- until the sharing is correct. For both springs and resistors, the speed at which they bounce back and forth until they settle is called the 'wave speed'.

If you have the correct test equipment, and the correct test material, you can measure the voltage equalizing down a string of resistors when you connect them.

• I think this is a poor analogy, when there are better hydraulic analogies available. A battery is not like a bucket. There is no air in an electrical circuit, and the electrical charge must return to the battery, not simply fall to the ground. amasci.com/miscon/elect.html – Phil Frost Feb 23 '13 at 13:08

Think of a battery as a pump for a fluid of electrical charge. It generates a difference in pressure from one side to the other (the voltage), and in doing so, the electrical charge is made to move through the pump and the circuit connected to it.

Let's think of resistors instead of LEDs. A resistor is like a hose. Current can pass through it, but friction causes the pressure on one side of the hose to be higher than the other. A high-valued resistor is like a small hose with a lot of friction. A low-valued resistor is a large hose with less friction. A wire is a hose that's so big that the friction is negligible.

If you connect three hoses or resistors in series, their resistances add, and they provide more resistance as a unit to the current than one would alone. Although the pressure the pump is generating hasn't changed, less current will flow. If the hoses or resistors are identical, the resistance will be three times as much as just one.

If you connect three hoses in parallel, this is like connecting one bigger hose instead. The pressure generated by the pump still hasn't changed, but now more current can flow. The resistance will be one third that of one hose or resistor, if they are identical.

Another way to think about it: all of the current for each of the three identical parallel hoses must come from, and return to the pump. Each hose still sees the same pressure as it would see if there were only one hose, so the same current will flow in that hose. But, the current in the pump must be three times what it would be with one hose, because there's no other place for the current to go. In electrical systems, this is formally explained by Kirchoff's laws.

This drains the battery faster because power, the rate of energy conversion (electrical energy is converted to heat in a resistor), is current times voltage:

$P = I E$

If voltage is in volts and current in amperes, then power is in watts. Mechanical systems have power also in watts. For example, power equals force times velocity:

$P = F v$

You can push something just a little but really fast (say, lifting a tennis ball), or push something really hard but very slowly (lifting a car with a jack) but the power can be the same. Of course, lifting a car takes more energy than lifting a tennis ball, and this is why it takes longer to lift a car: at low power, it takes longer to accumulate enough energy conversion (chemical energy from food to gravitational potential energy) to lift the car.

So, for something like a battery, where the voltage (electromotive force) remains roughly constant, the rate at which it is drained is proportional to the current. Power is the rate the battery converts its chemical energy to electrical energy.

To apply this to LEDs, consider an LED as a check valve. It's a diode, and it limits current flow to only one direction. It takes some amount of pressure to open the valve (the forward voltage drop), but beyond that, more current can flow without significantly more pressure being lost over the check valve. This is why an LED needs some device (often a series resistor) to limit the current: if the battery voltage is more than the forward voltage of the diode, then a ton of current can flow, probably more than the diode is designed to handle, and it will break.