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Wires and Voltage Ratings Calculation

CABLES DIMENSIONING

This is a method to help on calculations relative to the electric cables dimensioning in the direct current operating systems.
From the following formulas it is possible to obtain:

Each conductor, depending on its section, gives a certain resistance to the passage of current. The following is a table that summarizes the specific resistance values for the copper cables and the sections more usually used.

Cable section in mm2Specific resistance
0,220,090
0,500,035
1,000,018
1,500,012
2,000,009
2,500,007
3,000,006

Definitions

  • V. drop: Voltage drop on the load (difference between the output tension from the supplier and the minimum operating tension of the connected device)
  • Length: Line length ( distance from the supplierx 2 ) in metres
  • I. load: Max. Current drawn from the device connected in the end of the line ( in mA )
  • Section: Section of the cable used ( which corresponds to the specific resistance as shown in the table above) in mm2

Calculation of the VOLTAGE DROP

 (Specific resistance x Line length) x I.load 
V. drop =

= Volt
 1000 

EXAMPLE
A sounder that draws max. 2A must be installed on a 100 metres line. The line is installed using a cable with a section of 1 mm2.
Which voltage drop will be in the end of the line?
Solution: ( 0,018 x 200 ) x 2000 / 1000 = 7,2 Volt


Calculation of the maximum current allowed in the end of the line

 V. drop max allowed x 1000 
I.load max =

= mA
 Specific resistance x Line length 

EXAMPLE
Is it possible to install a 24 V sounder that draws 2A max. in the end of a line 100 metres long using a cable with the section of 1 mm2 taking into consideration that the sounder operates with a minimum of 13 V ?
Solution:
( 24 - 13 ) x 1000 / 0,018 x 200 = 3055 mA = 3 A .... so the answer is : YES.

And if the sounder operates with a minimum of 18 V ?
Solution:
( 24 - 18 ) x 1000 / 0,018 x 200 = 1666 mA = 1,6 A .... so the answe is : NO.


Dimensioning of the CONDUCTORS SECTIONS  that supply a sensor or a call point

Together with the choice of the battery capacity and the definition of the current suppliable by the supplier, the correct dimensioning of the cables sections allows the devices to have optimal tension values according with the regulations established by the manufacturer.
Supplying a sensor or a call point with a lower tension than the minimum value stated means for the device a situation of instability, low efficiency, poor immunity to the noises.

The following data must be considered:

   Example
Voltage at SourceVsFor a correct and preferable result consider a critical situation as mains loss24 V
Minimum voltage on sensorVcPointed out by the manufacturer data13,5 V
Sensor currentIcRefer to manufacturer data sheet or measured by a multimeter (in milliampere)
NOTE: In the case of NOT self-powered devices must be used the higher absorption in the different conditions: Service, Stand-By, Alarm
10 mA
Line lengthLSegment of cable between the source and the sensor (in metres)50 m

Calculated the data, they can be insert in an easy formula to obtain the measure of the smallest cable section that is able to guarantee the optimal functioning: the minimum section, measured in mm2, must be equal or bigger than:

Section = ( 2L x Ic x 0,038 ) : [ ( VS - Vc ) x 1000 ]

EXAMPLE
Section = (100 m x 10 mA x 0,038 ) : ( 24 V - 13,5 V) x 1000 ) = 0,0036 mm2

The cable for the installation must have the conductors section equal or bigger than 0,04 mm2

The method described can be used to dimension with a good approximation a more complex tension network, with ramifications.
In this case it is enough to identify all the connection points from the source on, to effect the calculation for each single segment between two points and then summing all the results.

IMPORTANT NOTE
Take always into account the minimum sections given by the bodies of regulations that happen to be bigger than those obtained from the calculations.


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