Why does voltage drop become more noticeable in longer LED circuits?

[cedricuk]

I've been trying to understand voltage drop in longer low-voltage LED circuits from a physics perspective.

If the supply voltage is constant, increasing the length of the conductor increases the total resistance. With the same current flowing through the circuit, this should produce a larger voltage drop according to Ohm's law.

What I'm less clear about is how this develops along the length of a circuit rather than simply appearing as a single voltage loss. Does the potential decrease continuously along the conductor, and can this be thought of as an electric field driving the current through the resistance of the wire?

I'm also interested in how the wire's cross-sectional area changes the situation. A thicker conductor has lower resistance, but is there a useful way to relate this directly to the potential gradient along the conductor?

I'd appreciate an explanation from the physics side rather than just a practical wiring rule.

 

[Baluncore]

If the supply voltage is constant, increasing the length of the conductor increases the total resistance. With the same current flowing through the circuit, this should produce a larger voltage drop according to Ohm's law.

The same current does not flow in the circuit.

The supply voltage is fixed, Vs.
The LED voltage is fixed, Vd, (by the band gap of the material).
The resistance, R, of the circuit wires is proportional to length.
The current that flows in the circuit will be, I = ( Vs – Vd ) / R .

If you increase R, then I will fall.

 

[berkeman]

What I'm less clear about is how this develops along the length of a circuit rather than simply appearing as a single voltage loss. Does the potential decrease continuously along the conductor,

Yes. It's a little more complicated than that, depending on how the LEDs are driven. If they are simple LEDs each with its own series current-limiting resistor, then the current through each LED depends on the voltage available at the tap point where the LED and its series resistor are connected on the wires. So the LEDs near the end of the string will receive a lower voltage from the string wires, and will be a little dimmer than the first LED in the string.

If each LED has its own switching current source that draws power from the string wires, then the LEDs will be the same brightness even though the string wiring voltage decreases with distance. Each LED circuit will draw the same power from the string wiring, so the LED circuits at the end of the string will be drawing a higher current from the wires due to the lower voltage that they see. This is a non-linear effect that has some strange behaviors, which I can describe in more detail if you are interested.

 

[sophiecentaur]

If the supply voltage is constant, increasing the length of the conductor increases the total resistance.

Yes. That's correct. The resistance of the supply wires is set by the material (copper, mostly) and the dimensions. So far so good.
You mention Ohm's Law but that law only applies to ideal conductors like metals. An LED is far from ohmic so all the basic calculations you can do when adding resistances in series etc etc fail with semiconductor devices.
Also, as mentioned above, your regular DC power supply provides you with a constant voltage over a range of device resistances. You 'can' make 'constant current' power supplies and all the calculations need to be modified but that's what we would call "second year work" lol.

 

[DaveE]

Does the potential decrease continuously along the conductor,

Yes.

can this be thought of as an electric field driving the current through the resistance of the wire?

Sort of. Field descriptions can get complicated. I would stick with the voltage (potential) for now. The current would be determined by the entire loop circuit, so wires plus the devices (LEDs) that the current has to flow through.

Khan academy has some really good tutorials on electronic circuits.

 

[sophiecentaur]

Field descriptions can get complicated. I would stick with the voltage (potential) for now.

And why? It's because Fields are vectors and have direction so, in the end you'd need to consider the actual route of connecting wires and positions of components in your calculations. Using Potential (Volts) you are only concerned with the way the Electrical Potential Energy changes around the circuit. Electric Fields come into it in particle accelerators and Cathode Ray Tubes where the electrons tend to go in the direction of the field.

Khan academy has some really good tutorials on electronic circuits.

It's full of proper Physics, agreed, but the presentation is very pedestrian with writing on a white board etc.. You need to be very determined to get through it. But presenting the same content in a zippy way involves a lot of hard work from the presenter so its often necessary to do a lot of hunting for a more exiting alternative.

 

[Baluncore]

Where you have an end fed strip of many groups of LEDs, each group with a current limiting resistor, the voltage drop along the supply lines will result in some voltage variation along the strip. LEDs will be brighter at the feed end, dimmer at the open end.

One way to reduce that variation is to feed the strip from both ends. Connect the positive supply at one end, with the negative supply at the other end. That places the same series supply resistance in all LED current paths, so the voltage variation should not result in a current or brightness variation along the strip.

All LEDs will then be equally bright, the same brightness as the LED in the middle of the strip would be, if fed with both supplies from one end only.