Calculating A Cable Size

WORK IN PROGRESS

Choosing the right sized cable is not always as easy as it looks.

Selecting the correct cable for the application is imperative to ensure a satisfactory life of conductors and insulation subjected to the thermal effects of carrying current for prolonged periods of time in normal service.

Choosing the mimimum size cross sectional area of the conductors is essential to meet the requirements for

• Protection against electric shock
• Protection against thermal effects
• Overcurrent protection
• voltage drop
• Limiting temperatures for terminals of equipment to which the conductors are connected

How to size a cable

Differences between overcurrent and overload protection

All circuits are designed to protect the cables against overcurrent (eg a short circuit). However full overload protection is not always required or possible on some circuits.

Overload protection requires the cable be able to carry an overload that is 1.45 times the MCBs rated current. A typical example of this would be a lighting circuit with a 6 amp MCB. The circuit is designed to carry a maximum of 6 amps but the MCB will not trip instantly at 6 amps. In fact the MCB will take around 1 hour to trip when the current is (6 x 1.45)= 8.7 amps. Designing the circuit to carry 8.7A gives the overload protection needed should a householder change the light fittings for higher powered ones and start to exceed the 6A maximum design current.

Overcurrent protection is not provided when we know the fixed current of the appliance and we install a cable that is capable of carrying this current. A typical example of this would be an electric shower. We will show in the worked examples later on that it is possible to safely install an MCB that has a higher rating than the cable's maximum current rating.

Sizing conductors for your circuit

How to calculate Iz

• Iz is defined as the rated current carrying capacity of the chosen cable, for continuous service, under the particular installation conditions.

There are some other standard terms we can define, which we will need shortly:

• Ib - The design current of the circuit. This is the starting point for all the calculations. Ib is calculated by dividing the power of the appliance (W) by 230 (the nominal voltage).
• In - The rated current of the protective device. This is usually the MCB with the closest rating to Ib where In > Ib
• It - The tabulated value of the current carrying capacity of the cable. For T&E cable It is taken from this table.
• I2 - The actual operating current of the protective device. For a MCB, I2 is 1.45 x In. Note I2 is only needed if overload protection is required

Having calculated the easy bits: the design current (Ib) and then protective device rating (In) we now need to calculate Iz.

Iz may be found in two ways. For both methods if full overload protection is required then Iz must be >= I2

Where overload protection is not required then Iz may take two possible values. The best way is to calculate for Iz >= In. However we actually only need to calculate for Ib <= Iz <= In.

Method 1

With direct reference to the table. If the cable is installed ungrouped, in an ambient temperature of 30C, 
and  is protected by a B type MCB, then Iz = It and the cable size is chosen by looking down your reference method column to
find Iz.

Method 2

Iz is calculated by using the formula

Iz = It x Ca x Cg x Ci x Cr

Where It is column C of the table.


Ca is a correction factor due to the ambient temperature (values from table 4C1)

Cg is a correction value for cables grouped with other circuits (values from table 4B1)

Ci is a correction value for cables in insulation 

Cr is a correction factor of 0.725 for BS3036 fuses

Checking Voltage Drop

For lighting circuits the maximum volts drop is 3% (6.9V) and for all other circuits the maximum voltage drop is 5% (11.5V).

We now need to test that the chosen cable will be big enough to supply the circuit without dropping the maximum allowed voltage drop. The table below shows the voltage drop in mili Volts (mV) per amp, per meter. So to find the total drop simply multiply this value by the design current Ib, and the length of the cable L:

Total voltages drop = (Voltage Drop x Ib x L)

This will give the voltage drop in mV. Divide by 1000 to convert to Volts 

Conductor CSA (mm²)	PVC (max 70° C) Voltage drop mV/A/m
1.0	44
1.5	29
2.5	18
4.0	11
6	7.3
10	4.4
16	2.8

Worked Example

Say we have an electric shower with a design current Ib of 41A, and a cable run of 15m, installed using Method C. Initial 
checks would suggest that 6mm² T&E will be adequate. From the table above we know that 6mm² will drop 7.3 mV/A/m. So:

Total Drop = 7.3 x 41 x 15 / 1000 = 4.49V which is acceptable

Worked Examples

More to follow...