So far we have learned that the thickness of a wire (cross-section) is chosen based on how much current we want to pass through it (the Amperes) so that it does not heat up and melt. But what happens when the current has to travel very far?
Imagine you want to power a warehouse in your garden, a water pump on the estate, or put floodlights on the front door, 50 meters from the house. Your electrician says he's going to put in "thick wire" even though the projector burns minimal current. Is he trying to overcharge you for materials?
No. It tries to fight the biggest enemy of long distances: Voltage Drop. As engineers, let's take a look at why this phenomenon occurs, why it burns the motors of your devices, and how we calculate it with simple math.
Think of current like water running through a watering hose. If you have a very long hose (eg 50 meters), the water pressure at the end of it will be significantly less than the pressure at the tap. The water was "tired" by rubbing against the walls of the pipe all this way.
It is exactly the same with electricity. Copper wires are excellent conductors, but they are not perfect. They have a small, natural resistance. The longer the cable, the greater this resistance. As the current travels through it, it loses some of its power (turns into heat). The result? While your electrical panel sends out 230 Volts, the edge of the garden may only get 190 Volts!
If the voltage (Volt) reaching your device is too low, the problems start:
If you connect a water pump, lawnmower or washing machine to the end of a very long cable, the motor will get low voltage. To get the same power, it will have to "pull" more Amperes. It will overheat and gradually burn out.
Bulbs (especially older ones) will glow very dimly or flicker.
The voltage that was "lost" along the way, turned into heat in the soil. It is electricity that you pay to DEDDIE, but it never reached your device.
The electrical regulations (such as the ELOT HD 384 / 60364 standard) are strict. They stipulate that the voltage drop from the DEDDIE meter to the furthest socket or lamp in your home must not exceed certain percentages:
Maximum allowable drop of 3% (ie, maximum 6.9V loss at 230V).
Maximum allowable drop of 5% (ie, maximum 11.5V loss at 230V).
To find how many Volts we will lose, we use the following formula (for single-phase alternating current). The equation includes the current, the distance and the thickness of the wire:
Delta U = frac2 cdot I cdot rho cdot LS
Where:
(Note: The multiplication by 2 is done because the current has to go from the Phase and return from the Neutral, so it travels twice the distance).
Scenario 1 (We put in the standard 2.5 mm² plug cable): Delta U = frac2 cdot 16 cdot 0.0175 cdot 502.5 Result: Delta U = mathbf22.4 Volt. What does this mean? You lost 22.4V! Only 207.6 Volts reach your warehouse. The loss is almost 10%, more than twice the permissible limit (5%). Your tools will be dangerously strained.
Scenario 2 (We put thick cable 6.0 mm²): Delta U = frac2 cdot 16 cdot 0.0175 cdot 506.0 Result: Delta U = mathbf9.3 Volt. What does this mean? The loss fell to 4%. We are within the legal limits and our machines are absolutely safe!
The Voltage Drop in Volts (the number we are looking for).
The Current that the device will draw in Amperes.
The resistivity of copper (a constant approximately equal to 0.0175 Omega cdot mm^2 / m).
The length of the cable in meters (m).
The cross-section (thickness) of the wire in square millimeters (mm^2).
You want to pull a supply to a warehouse, 50 meters away. You'll be working powerful power tools there, so you want a full 16 Amperes (3,680W) supply.
As we proved with mathematics, the solution to the voltage drop is one: The longer the distance, the thicker the cable must be, even if the current we need is small. A larger "tube" (larger cross-section S) offers less resistance to the current, allowing it to reach its destination without loss.
In closing this sub-pillar of calculations, remember: Electricity is not just "putting wires together to light a light bulb". It requires foresight. When planning exterior lighting, end-of-lot garage door supplies, or security camera lines, discuss the voltage drop factor with your installer to ensure longevity of your expensive equipment.
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