2.1 Introduction

Electrical engineering is primarily focused on power generation and consumption.

It is important to understand some key concepts with most concepts mathematically based. Electrical power system are commonly grouped into AC and DC systems. AC systems are further broken down into single phase and three phase.

We will focus mainly on power systems.

2.2 Power and Energy

Electrical power and energy are not the same. Power is an instantaneous value akin to the speed you are doing on a motorway. Energy is the culmination of this power over time. This is akin to the distance you have traveled. Energy is the ability of an entity to do work

A key understanding of energy is work. Work is the force applied to an object over a distance.

$$U=F·l$$

Where:

U = Work.

F = Force (newtons).

l = Distance (metres).

If we move an object through 1 metre using a force of 1 Newton, the amount of energy we used is 1 Joule. 1 Joule is also 1 Watt of power consumed in 1 second.

$$\mathrm{1J}=\mathrm{1N}·m$$

$$\mathrm{1J}=\mathrm{1W}·s$$

Where:

J = Joule.

W = Power (watts).

s = second.

Often in power systems we talk about energy in kWh (kilo watt hour) or MWhr (mega watt hour). Your electricty bill will almost certainly be charged on energy in one of the above values.

$$\mathrm{1\; kWh}=\mathrm{1000\; watts\; consumed\; in\; 1\; hour}$$

$$\mathrm{1\; kWh}=\mathrm{1000W}·\mathrm{60s}·\mathrm{60m}$$

$$\mathrm{1\; kWh}=\mathrm{1000W}·\mathrm{3600s}$$

$$\mathrm{1\; kWh}=\mathrm{3.6}x{\mathrm{10}}^{6}J$$

Energy sometimes uses calories. 1 calorie is the amount of energy needed to raise 1 gram of water 1 degree Celsius. Since this is small value often kilo calories are used whereby 1 kilo calorie is the energy needed to raise 1 litre of water 1 degree C.

$$\mathrm{1\; calorie}=\mathrm{4.186\; J}$$

$$\mathrm{1\; kilo\; calorie}=\mathrm{4.186\; J}·\mathrm{1000}$$

$$\mathrm{1\; kilo\; calorie}=\mathrm{4.186\; kJ}$$

Worked Example

An example is the best way to demonstrate this. Lets say we have a 750 watt pool pump that runs for 3 hours every day, 7 days a week. We want to work out what the power is and energy consumed over 1 day. Lets assume our power bill is sent out every 90 days and the power company charges us 32 cents per kWhr. Find out what the total cost of running this pump is over 1 billing period.

Since the pump is quoted in Watts, we must convert to kilo watts by dividing by 1000 because we are billed in kilo watt hours (kWhrs).

Where:

Power = 0.750kW This is the power consumed by the pump

The pump runs for 3 hours every day. So the power consumed is the instantaneous value which is 750 W. The energy is the power consumed over the 3 hours.

$$\mathrm{Energy}=\mathrm{Power\; (kW)}·\mathrm{Time\; (hours)}$$

$$\mathrm{Energy}=\mathrm{0.75kW}·\mathrm{3h}$$

$$\mathrm{Energy}=\mathrm{2.25\; kWhr}$$

We can also work out the energy in kilo joules to see how many Arnotts Wagon Wheels we must eat if we powered this pump by human power.

$$\mathrm{Energy}=\mathrm{2.25kWhr}·\mathrm{3.6}·{\mathrm{10}}^6$$

$$\mathrm{Energy}=\mathrm{8.1}·{\mathrm{10}}^6\mathrm{Joules}$$

$$\mathrm{Energy}=\mathrm{8,100\; kJ}$$

Or in kilo Calories.

$$\mathrm{Energy}=\frac{\mathrm{8,100}}{\mathrm{4.186}}=\mathrm{1,935\; kCal}$$

Since each Arnotts Wagon Wheel 48g biscuit contains 864kJ, we can eat 9.3 Arnotts Wagon Wheel 48g biscuits and get on a treadmill with a generator to run our pool pump for 3hrs.

Next we need to calculate the energy over the billing period.

$$\mathrm{Energy\; over\; 90\; days}=\mathrm{2.25kWhr}·\mathrm{90\; days}$$

$$\mathrm{Energy\; over\; 90\; days}=\mathrm{202.5kWhr}$$

$$\mathrm{Cost\; over\; 90\; days}=\mathrm{202.5kWhr}·\mathrm{32\; cents}$$

$$\mathrm{Cost\; over\; 90\; days}=\mathrm{6,480\; cents}=\mathrm{\$64.80}$$

So your pool pump cost $64.80 over the 90 day billing period if we ran it for 3 hours each and everyday over the billing period and assuming our tariff was constant at 32 cents per kWhr. Or you can eat 9.3 Wagon Wheels and jump on a treadmill generator every day and then over 90 days, consume 90 x 9.3 = 837 Wagon Wheel biscuits to avoid the bill! Click here to go to calculators.

2.3 Volt and Electro Motive Force

In order for electricity to flow, it needs a force. This is EMF. EMF is measured in Volts. EMF can be generated in several ways but the most common are:

• Electro chemical - This is seen in common batteries like lead acid, Lithium ion etc
• Photo voltaic - This is commonly seen in solar panels.
• Electro Magnetically - This is commonly used in rotating plant to convert mechanical energy.
• Piezo - This is commonly seen in piezo electric via stress (mechanical or temperature).

EMF is practically either AC or DC. AC being an acronym for Alternating Current and DC being an acronym for Direct Current.

We can see from above that an AC voltage and current swings about the 0 volt line alternating from positive to negative. In a DC circuit, the voltage and current stays on one side whether positive or negative.

2.4 Electrical Basic Elements

Electricity has a number of basic level components that define pretty much all circuit network theory. They are:

• Resistors - Components that resist the flow of current and convert electrical energy to heat.
• Inductors - Components that convert/store electrical energy to/in magnetic fields.
• Capacitors - Components that convert/store electrical energy to/in electric fields.

2.4.1 Resistors

Resistors are perhaps the simplest element to understand. They simply resistor the flow of current and dissipate the energy as heat. Resistors are usually specified with three parameters:

• Resistance - Ohms. This is the value of the resistor.
• Wattage - Since resistors dissipate the energy as heat they must be specified with a wattage rating.
• Tolerance - This is the percent tolerance usually ± as a % of the resistance.

Common electronic resistors are 0.25 Watt or even less. Sometimes you see 0.5 or 1 W and then beyond this the resistor moves to a ceramic package and then higher up, it is common to see wirewound. Common electronics will use 0.25W with ± 0.1%

For more information on resistors, click here.

2.4.2 Inductors

Inductors are essentially coils of wire that form a magnetic field. This element ideally does not dissipate any energy. It stores the energy in the magnetic field.

Inductors are used primarily in AC circuits where the current alternates and the magnetic field alternates. This is because in the DC circuit, an inductor appears as a short circuit. When a DC circuit is swtiched on or off, there is a time change component in the circuit current and inductors have an impedance to time varying currents.

The inductor is specified in Henries

For more information on inductors, click here.

2.4.3 Capacitors

Capacitors are arguably the opposite of inductors. They are essentially a plate of conductive material that forms an electric field. This element ideally does not dissipate any energy. It stores the energy in the electric field.

Capacitors are used primarily in AC circuits where the current alternates and the electrica field alternates. This is because in the DC circuit, a capacitor appears as an open circuit. When a DC circuit is swtiched on or off, there is a time change component in the circuit current and capacitors have an impedance to time varying currents.

The capacitor is specified in Farads