Why do electricians use math?

1) Why is math important for electricians? 

There are many times when an electrician will need to use mathematical calculations in order to perform their job safely. Math is VITALLY important for electricians to be able to use and understand. It is not only important to be able to carry out the calculations but also for the electrician to understand WHAT they are doing and WHY they are doing it. 

The ability of an electrician to use graphs, charts and tables matters, because a mistake could literally cost lives or ruin electrical systems and buildings. 

2) To be able to perform basic calculations

At the heart of every electrical job there are the requirements for calculating electrical variables such as Resistance (measured in Ohms) which is the impedance to electrical current flow. Current (in Amps) which is the flow of electrical charge in a circuit and Voltage (in Volts) which is the electrical ‘force’ or ‘pressure’ pushing the electrical current around the circuit. 

These components make up the workings of every electrical system, with these three things operating in harmony, electrical systems function with ease. Without the ability to work out these three things an electrician would struggle with the requirements that follow such as the ability…..

3) …..To check the total length of an electrical circuit

When an electrician designs an electrical circuit there are many factors that come into play in order to ensure that the design is safe. One of these factors is the LENGTH of the cable. As an electrical cable gets longer there is an increased resistance to electrical current flow. It becomes harder for electrical current to move down the circuit the farther it has to go.

Think of jogging to the end of the street, just a few hundred yards, right? Then think of jogging a marathon. The longer the distance the more difficult it becomes to reach your destination. 

Using Math is the only way to check that the cable length will not prove too much of a problem for the electrical current to flow. 

4) How does the electrician do this?

Electricians have manuals and regulations books that tell them how much resistance each type of cable has per metre. When an electrician designs an electrical circuit, they use these manuals to determine what the maximum length of the circuit could safely be before there are other design problems. 

5) To calculate the maximum load on cables

Copper is normally the preferred material for electrical cables. Copper is very conductive (good at allowing electrical current to flow) and is not as expensive as other conductive materials. There are specific tables in the manuals that state the resistance of copper cables per metre, at each size that is manufactured. The thicker the cable the lower the resistance and also, the more electrical current it can safely carry. The downside is that it gets more expensive so it’s important that ELECTRICIANS USE MATH wisely to keep costs down whilst still designing safe electrical circuits. 

When an electrician designs an electrical circuit, part of the consideration is for the electrical load that will be placed on the circuit. The greater the electrical load the more powerful the circuit needs to be and the larger the panel breaker or circuit breaker will need to be. The cable will also need to be suitably sized in order to carry this electrical load without overheating or becoming a danger. 

When calculating the maximum load on a cable the electrician refers to the tables in their manuals to find the maximum current carrying capacity of the cables. A circuit that feeds only ceiling lights around the home will not demand much electrical current, even with all lights in use. As such, a smaller cable and panel breaker can be selected for these types of circuits. 

6) To work out the correct size of cable to use

When selecting the cable size, the electrician adds up all the electrical loads and determines how much electrical current is likely to be needed at ‘peak demand’. 

If we think about peak demand for a moment then we can imagine a busy household at dinner time with all the lights on, the dishwasher, dryer, washing machine, kettle, ovens, toaster, and many other appliances that will be in use. 

This is a time of peak demand and the cables need to be sufficiently large in order to serve up the necessary electrical current for all this equipment. 

In a busy household, the kitchen tends to demand the most power and the cables selected are done so to ensure that they will not overheat during these busy times. 

7) To determine which panel breakers are needed

Along with selecting the correct cable sizes for the electrical circuits and the electrical loads, the panel breakers must also be selected correctly. The panel breakers or circuit breakers each have an electrical current rating. This rating is the amount of current that they will safely allow to pass before they start to trip off. 

A 32-amp circuit breaker will safely allow up to 32 amps of electrical current to pass. Once the electrical current exceeds this amount then the circuit breaker will begin trip. The higher the demand current rises above this 32-amp limit, the quicker the circuit breaker will trip. 

The cables will be selected to ensure that they can safely carry this 32 amps and a little above until the circuit breaker trips. 
If too large a panel breaker or circuit breaker is chosen for a given cable size then the cable is likely to overheat or catch fire before the breaker trips the circuit off. If too small a circuit breaker is chosen for a given cable size, then the cable will never be able to deliver its full potential and there will possibly be problems with the circuit tripping off too early meaning not all appliances can be used at the same time. 

8) To make sure the circuit disconnects when it needs to

That’s right. A lot of these calculations for cables, panel breakers and circuit lengths are all done to make sure that the electrical circuit will disconnect when it needs to. 

We need to make sure that the panel breaker or circuit breaker is able to disconnect the circuit quickly when there is an electrical fault. 

9) WHY DO ELECTRICIANS USE MATH? 

We calculate the circuit length and obtain the maximum resistance of the circuit at the furthest point. We add this resistance to the EXTERNAL resistance of the cables in the street and back to the electrical supply transformer at the end of the road or block. 

When we have this total resistance, we use OHMS LAW to determine how much electrical current could flow in the event of an electrical fault. We want enough electrical current to be able to flow to turn the circuit breaker off quickly. 

The greater the resistance of the electrical circuit THE LOWER the electrical fault current. 

So longer circuits with an electrical resistance that is too high will not turn the circuit off quickly enough when there is an electrical fault. That means the cables will overheat, melt, catch fire and generally go wrong. It’s important that the electrician designing the circuits takes all of these things into account BEFORE they install any electrical cables or panel breakers. 

A mistake in selecting the cable, the breaker or the electrical load could have DEVASTATING EFFECTS!

10) To be able to calculate angles

There are occasions when an electrician will need to measure and calculate angles in order to install ‘pipe’ or conduit systems. Being able to correctly measure angles will ensure that cable containment systems are able to be cut and bent correctly first-time saving labour, materials and therefore money. 

Calculating angles can also help with estimating light dispersion from a luminaire over distance. Checking to see if a movement sensor will detect movement in the areas that is required by checking the manufacturer’s instructions, measuring the angle, and comparing to the area requiring movement cover. 

11) To find electrical faults

When there is an electrical fault on a circuit the panel breaker or circuit breaker should trip. When this happens the electrical supply to the circuit is disconnected and the circuit is once again made safe. In order to safely restore the electrical supply to the circuit the electrical fault must be found. 

Generally, there are a few different kinds of electrical faults that are likely to trip a circuit breaker or panel breaker. These are classified into two types:

1. Overload current faults
2. Fault Current faults

1     An overload current is an electrical current that is taking place in an electrical circuit that is otherwise electrically sound. When an overload current is occurring, too much electrical current is flowing in the circuit. This is normally through the use of too many appliances in use at the same time. Example, washing machine, tumble dryer, clothes iron, electric oven, bread toaster, kettle and so on. When this situation occurs, we are likely to see the circuit trip after a short while. 

The circuit will generally trip after several seconds to a couple of minutes of this type of use. This is not a very dramatic type of electrical fault and the panel breaker or circuit breaker is likely to gently click off.

There is generally no need to dismantle an electrical circuit to discover the cause of this type of fault. One method of determining if there is an overload current through the excessive use of electrical appliances if for the electrician to use their clamp meter. 
The clamp meter is a device that measures the current flow in the circuit, the electrician can compare the maximum current flow with the rating of the circuit breaker and is then able to determine if too much electrical current is flowing in the circuit. 

2    When a fault current is occurring there is generally a very large electrical current occurring in the circuit. This type of electrical fault will cause the panel breaker or circuit breaker to operate more violently as it disperses the large electrical current through its internal mechanism. The energy dissipation is converted from electrical energy into heat and sound. 

This type of electrical fault results when there is a very low electrical resistance in the circuit between Line (LIVE, PHASE, HOT) and either Earth (Ground) or Neutral. 

When two wires in an electrical circuit touch, there forms a very low resistance which means a large amount of electrical current can flow momentarily until the circuit breaker trips and the electricity supply to the circuit is disconnected. 

With this type of fault, the electrician is able to use their knowledge of math and test the circuit to see if there are any unwanted connections. They will also be able to measure the resistance of the unwanted connections and calculate the fault current that would flow should the circuit be reinstated. 

In an electrical circuit that had equipment connected, we would see a resistance between LINE and NEUTRAL as there would be items such as lamps, appliances and other electrical equipment that would give a resistance reading. These values would typically be too high a resistance to generate a fault current. There should generally be no low resistances between any of the three conductors (LIVE, NEUTRAL, EARTH) in a circuit as such circumstances would cause electrical fault currents. 

We can now start to see some answers to WHY DO ELECTRICIANS USE MATH 

12) To make sure equipment functions correctly and receives the right voltage

Earlier in this article we touched on circuit length and resistances. Whilst these are important, we must also consider voltage drop.

What is voltage drop?

Voltage is the electrical force that pushes electrical current along and helps it overcome resistance. The greater the voltage, the smaller the cable needs to be in order to transport electrical current and the easier a current can flow in the face of resistance. 
To that end, we must make sure that the circuit is not too long. Not only for the sake of resistance but also for voltage drop. When more electrical current flows through a cable this can also adversely affect the voltage. 

There is a tolerance that is allowable for voltage drop. This is typically around 3% for lighting circuits and 5% for power circuits (anything other than lighting). This is to ensure that electrical equipment receives the correct voltage and will work as intended. If the voltage is too low then things may not work, lights may dim or not come on and appliances and equipment will wear out quickly. 

The solution? 

Lower the electrical load, reduce the distance, or increase the cables thickness to compensate for voltage drop.

13) To calculate the maximum demand of the installation

Every electrical installation will have a MAIN FUSE installed in the incoming supply equipment. This fuse is to protect the incoming supply cable from overload and failure. If too much electrical current is used in the installation, then the main fuse will eventually blow and disconnect the electrical supply to the installation. 

Every electrical installation should be designed such that the maximum demand of the installation does not exceed the rating of the main fuse that protects the supply to that installation. The electrician needs to be able to calculate (or estimate with reasonings) the maximum electrical current that would be required in each electrical installation during peak times. 

This is not an easy thing to do in lots of cases as there is no real knowing how the electrical installation will be used! There is some guidance in the electricians’ manuals as to what is likely to be the maximum demand of each electrical circuit and then, as a result, the maximum demand of the whole electrical installation but it is not foolproof. 

WHY DO ELECTRICIANS USE MATH? The reasons for this just keep on coming, don’t they?

14) To check that external factors do not affect cables capacity to carry electrical current

When an electrician designs an electrical installation, they need to consider what external factors may affect that system. There are various external influences that can affect a system and the ability of cables to safely carry electrical current. 

• Heat – When cables carry electrical current, they need to be able to get rid of the heat that is generated in this process. If extra heat is added in to this mix, then the cable is already at a disadvantage before any electrical current even begins to flow down there. If the cable is likely to be installed in an environment that is hotter than normal or would see ambient temperatures above typical temperature then the calculations would need to take account of this external influence. The electrician will calculate how severely the warmer environment or temperature will affect the cable and allow for this in their system design.
• Bunching or Grouping – When cables are installed together, they all have heat that needs to be dissipated. This can be aggravated when they are also installed in some form of containment such as trunking or conduit. Each cable has the need to dissipate its heat and with other cables surrounding it needing to dissipate their heat then issues can arise. 
• Insulation – Thermal insulation protects building from energy loss in the form of heat escape or heat entry. It manages this by refusing to allow much heat to pass through its structure. The thicker the insulation the less heat is transferred from one place to another. Cables surrounded, touched, or passing through thermal insulation cannot get rid of their heat efficiently whilst in contact with this material and as a result their ability to carry maximum current is affected! 

The solution to the current carrying capacity problems caused by these external influences is often to avoid them in the first place or as a last resort, to increase the thickness of the cable to cope with the lack of heat dissipation. This enables the cables to carry the current it needs to.

15) To determine if protective conductors are sufficiently sized

The ground (Earth, Circuit Protective Conductor) of a circuit is usually inside the cable itself. This wire needs to be sufficient in size to transport any fault currents in a circuit for the required time before the circuit is able to shut off. 

The protective conductor size is normally calculated by the cable manufacturer and then the cable is manufactured. There are occasions that the size of this conductor will need to be selected by the electrician and in order to do so they will need to calculate the size required. 

The earthing conductor for the installation will also need to be of a suitable size in order to sustain any fault current long enough to blow the main supply fuse if required.  

16) To check if there will be enough cable for a job

This is a more basic requirement but still a requirement nonetheless. When surveying a property for a new electrical installation or a rewire it is VITAL that measurements and calculations are done in order to obtain the quantity of materials required. 

Adding up the correct quantity of plug sockets and light switches so the right order is placed at the electrical wholesaler requires math. 

Checking the proposed cable routes and measuring to be able to get the correct lengths of cable for the job is, again, VITAL. 
Without using MATH, electricians would not be able to order the supplies to get the job done. 

17) To check the sizes of buildings and rooms

Along with the cable routes and quantity of materials, there is a need to check the sizes of rooms and buildings. This is especially important at the design stage of the wiring installation as there could be excessive circuit lengths that require more consideration. As circuits grow longer, the cable thickness should increase in order to safely carry the same current as a shorter circuit of the same rating. 

Higher ceilings may mean the need to obtain access equipment. Without calculating the required height of scaffold for example, it would be tricky to order the right scaffold towers. Without the correct height steps, attic or loft access would be unsafe. 

18) To calculate the brightness requirements in rooms for lighting

In lighting installations, there is a requirement to make sure that the lighting actually does its job. This requires some thought and some calculation. 

Let’s take a kitchen in the home for example. Many clients request downlights in their kitchen these days and when done right they can look great and give the right amount of light for the client’s needs. When done incorrectly there can be issues. 

The electrician needs to be able to calculate the correct distance away from the top kitchen cupboards to ensure that there is sufficient light at the worktops and counters without casting a shadow of the person standing in front of them. Too close to the wall and valuable light would be lost illuminating the top of the cupboards, too far away and the angle of light would mean dark shadows on counter tops whilst trying to read recipes or bake cakes.

Then there is the intensity of light that may be required in a building. With higher ceilings come challenges receiving sufficient light at floor level. With distance, the intensity of light drops. The further away the light source from the surface or object that needs to be illuminated, the greater the intensity of light that is needed. 

As light travels it spreads out decreasing the intensity.

19) The time that a job is likely to take and job planning

Another instance where math is needed would be job planning and time management. 

Every electrical job has one thing in common, it all takes time. Customers will tend to underestimate, massively, the time that a job is likely to take. Contractors will also do this but for different reasons. 

Each aspect of an electrical job can be broken down into sections and all these sections can be allocated a time. Calculating the total time for a job to be carried out requires math to be used. 

If we look at the example of a simple rewire:

• Time taken to travel to the quote 15 minutes x 2 = 30 minutes
• Discuss the customers’ requirements with them = 30 minutes
• Check cable routes and new locations for equipment = 15 minutes
• Research and calculate the cost of materials and produce a quote = 30 minutes
• Answer customer queries regarding quote and adapt any changes = 30 minutes

We can see quickly that the ‘quick quote’ is already likely to take over 2 hours in total.

Then when carrying out the job it is important to calculate the time it will take along with any unforeseen problems so the work can be profitable and not run over on schedule. Running over on schedule will mean other customers jobs have to be put back and this can become a mess quickly. 

It is important that an electrician uses math to calculate the overall time involved in each job from start to finish. Not doing so is likely to cost the business money and reputation in the long run. 

20) The cost of a job including labour and materials

This is one of the most vital parts of any electrician’s work. Calculating the overall cost of materials along with disposables and contingencies. Once the materials and labour has been accurately calculated the job quote can be put together along with a margin for profit to allow the business to expand, replace equipment and carry on trading. These figures are important to quote accurately as too high a job quote will mean that work is lost to cheaper contractors and too low a job quote is likely to land the business in a loss situation on the job. 

The time taken for sourcing and collecting materials needs to be assumed into the labour cost along with the time taken for handover to the client. 

The larger the business, the more important it is for these figures to be calculated accurately. Larger business sometimes operates on even tighter margins due to staff employment costs, extra taxes, and overheads and as such, a mistake in pricing over a few jobs can be devastating to the operation. 

21) To ensure that a business operates smoothly

Aside from job costs, an electrician may need to be able to calculate the correct percentage of each job to save in order to get the taxes right. There can be nasty surprises at the end of the year if the taxes have not been calculated correctly. 

Ensuring that the wholesaler is paid each month requires the ability to calculate how much to set aside from each job, on average, for wholesaler costs. In businesses with limited cash flow there can be issues paying for materials up front on every job. Regular payments on account calculated correctly can ensure that materials keep flowing and the business can continue to operate. 

22) WHY DO ELECTRICIANS USE MATH?

As we have seen, there are numerous reasons why an electrician would need to use math. The more technical aspects of electrical works will also require a greater understanding of mathematics and scientific concepts. 

Electrical design would be impossible without a firm grasp of maths and the ability to foresee potential installation issues that require workarounds. 

If one was considering a career in electrical installation, electrical design, or other discipline with electrical engineering then math is absolutely essential for success along with a good grasp of regulations, problem solving skills and logical thinking.