# Calculating voltage drops in cables with vectors?

• EVriderDK
In summary, the conversation discusses how to calculate the voltage drop in a 3x400VAC system using vectorial methods. The method involves finding the new voltage by subtracting the voltage drop from the nominal voltage, and this can be done by using the real and imaginary parts of the vectors. The conversation also mentions that power factor and trigonometric functions are important in understanding and solving these equations.

#### EVriderDK

Hey.

If i Have a 3x400VAC system, and I want to calculate the voltage drop over the cable "vectorially" - or what you call it :) - how do I do this?
U.nominal=400V

I have tried this method:
$\Delta$U.conductor=I.1*Z.cable1+I.2*Z.cable2+etc. and then I will have to find the new voltage ->
$\Delta$U.phase=U.conductor*$\sqrt{3}$
U.new=U.nominal-$\Delta$U.phase

When I'm calculating this with angles, I actually get a higher voltage, after the voltage drop :D
The voltage drop is cause by a electrical motor starting.

In school we learn it this way:
$\varphi$.motor=80 degrees

U.new=U.nominal-$\sqrt{3}$*I1*Length.cable1*(R.cable1*cos$\varphi$+X.cable1*sin$\varphi$)+$\sqrt{3}$*I2*Length.cable2(R.cable2*cos$\varphi$+X.cable2*sin$\varphi$)+etc.
But that is not with vectors.

Hope you understand?

Last edited:
I'm pretty weak with respect to power factor stuff, but sin and cos are intimately tied to the vector quantities.

Acosβ represents the X component and Asinβ the Y component of a vector of magnitude A at angle β (usually called real and imaginary parts).

If you want to add two vectors you can add their respective X parts and Y parts to determine the new X and Y parts of the resulting vector.

You can probably go through the equations you posted and see where the vector math is happening.

## 1. What is the purpose of calculating voltage drops in cables with vectors?

The purpose of calculating voltage drops in cables with vectors is to determine the amount of voltage that is lost or dropped as electricity flows through a cable. This information is important for ensuring the efficient and effective transmission of electricity.

## 2. How do you calculate voltage drops in cables with vectors?

To calculate voltage drops in cables with vectors, you will need to know the resistance, current, and length of the cable. Using Ohm's Law (V = IR), you can calculate the voltage drop by multiplying the resistance by the current and length of the cable.

## 3. Why is it important to calculate voltage drops in cables with vectors?

Calculating voltage drops in cables with vectors is important because it helps to ensure that the voltage at the end of the cable is sufficient for the electrical device to function properly. It also helps to identify any potential problems or inefficiencies in the electrical system.

## 4. What factors can affect the voltage drop in a cable?

The main factors that can affect voltage drop in a cable include the length of the cable, the amount of current flowing through the cable, and the resistance of the cable itself. Other factors such as temperature, material, and installation techniques can also impact the voltage drop.

## 5. How can you minimize voltage drops in cables with vectors?

To minimize voltage drops in cables with vectors, you can use thicker cables with lower resistance, reduce the length of the cable, and limit the amount of current flowing through the cable. Proper installation and maintenance of the cables can also help to minimize voltage drops.