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.