Electrical Energy and Power

Electrical Energy and Power

Electrical Energy supplies the power required to produce work or an action within an electrical circuit and is given in joules per second.

Electrical Energy is the ability of an electrical circuit to produce work by creating an action. This action can take many forms, such as thermal, electromagnetic, mechanical, electrical, etc. Electrical energy can be both created from batteries, generators, dynamos, and photovoltaics, etc., or stored for future use using fuel cells, batteries, capacitors or magnetic fields, etc. Thus electrical energy can be either created or stored.

We remember from our school science classes that the “The Law of the Conservation of Energy” states that energy cannot be created or destroyed, only converted. But for energy to do any useful work it must be converted from one form into something else. For example, a motor converts electrical energy into mechanical or kinetic (rotational) energy, while a generator converts kinetic energy back into electrical energy to power a circuit.

That is electrical machines convert or change energy from one form to another by doing work. Another example is a lamp, light bulb or LED (light emitting diode) which convert electrical energy into light energy and heat (thermal) energy. Then electrical energy is very versatile as it can be easily converted into many other different forms of energy.

For electrical energy to move electrons and produce a flow of current around a circuit, work must be done, that is the electrons must move by some distance through a wire or conductor. The work done is stored in the flow of electrons as energy. Thus “Work” is the name we give to the process of energy.

We can therefore say that Work and Energy are effectively the same as energy can be defined as “the ability to do some work”. Note that work done or energy transferred applies equally to a mechanical system or thermal system as it does to an electrical system. This is because because mechanical, thermal and electrical energies are interchangeable.

Electrical Energy: The Volt

As we now know that energy is the capacity to do work, with the standard unit used for energy (and work) being the Joule. A joule of energy is defined as the energy expended by one ampere at one volt, moving in one second. Electric current results from the movement of electric charge (electrons) around a circuit, but to move charge from one node to another there needs to be a force to create the work to move the charge, and there is: voltage.

We tend to think of voltage (V) as existing between two different terminals, points or nodes within a circuit or battery supply. But voltage is important as it provides the work needed to move the charge from one point to another, either in a forward direction or a reverse direction. The voltage, or potential difference between two terminals or points is defined as having a value of one volt, when one joule of energy is used in moving one coulomb of electric charge between those two terminals.

In other words, the Voltage difference between two points or terminals is the work required in Joules to move one Coulomb of charge from A to B. Therefore voltage can be expressed as being:

The Voltage Unit

electrical energy voltage unit

Where: voltage is in Volts, J is the work or energy in Joules and C is the charge in Coulombs. Thus if J = 1 joule, C = 1 coulomb, then V will equal 1 volt.

Electrical Energy Example No1

What is the terminal voltage of a battery that expends 135 joules of energy to move 15 coulombs of charge around an electrical circuit.

battery terminal voltage

Then we can see in this example that every coulomb of charge possesses an energy of 9 joules.

Electrical Energy: The Ampere

We have seen that the unit of electrical charge is the Coulomb and that the flow of electrical charge around a circuit is used to represent a flow of current. However, as the symbol for a coulomb is the letter “C“, this can be confused with the symbol for Capacitance, which is also the letter “C“.

To avoid this confusion, the common symbol used for electrical charge is the capital letter “Q” or small letter “q“, basically standing for quantity. Thus Q = 1 coulomb of charge or Q = 1C. Note that charge Q can be either positive, +Q or negative, -Q, that is an excess of either electrons or holes.

The flow of charge around a closed circuit in the form of electrons is called an electric current. However, the use of the expression “flow of charge” implies movement, so to produce an electrical current, charge must move. This then leads to the question of what is making the charge move, and this is done by our old friend Voltage from above.

So the voltage or potential difference between two points provides the required electrical energy to move charge around a circuit in the form of an electric current. Therefore the work done to move charge is provided by a potential difference, and if there is no potential difference between two points, there is no movement of charge and therefore no current flow. In fact, a charge without any flow or movement is called static electricity.

If the movement of charge is called an electric current, then we can correctly say that current is the rate of movement (or rate of flow) of the charge, but how much charge represents a current. If we select a point within a circuit, any point, and measure the amount of charge that flows past this point in exactly one second, this will give us the strength of the electrical current in Amperes, (A).

Thus one ampere of current is equal to one coulomb of charge which flows past a given point in one unit second, and the more charge per second which passes this point, the greater will be the current. Then we can define one ampere (A) of electrical current as being equal to one coulomb of charge per second. So 1A = 1C/s

The Ampere Unit

electrical energy ampere unit

Where: Q is the charge (in coulombs) and t is the interval in time (in seconds) that the charge moves. In other words, electrical current has both a magnitude (the amount of charge) and a specified direction associated with it.

Note that the commonly used symbol for electrical current is the capital letter “I“, or small “i” both standing for intensity. That is the intensity or concentration of charge producing the electron flow. For a constant DC current, the capital letter “I” is generally used, whereas for a time-varying AC current the lower case letter “i” is commonly used. The symbol i(t) means an instantaneous current value at that exact instant in time.

It is sometimes easier to remember this relationship by using an image. Here the three quantities of Q, I and t have been superimposed into a triangle represents the actual position of each quantity within the current formula.

The Ampere

ampere triangle

Transposing the standard formula above gives us the following combinations of the same equation:

ampere units

Electrical Energy Example No2

1. How much current flows through a circuit if 900 coulombs of charge passes a given point in 3 minutes.

electrical energy current flow

2. An electric current of 3 Amperes flows through a resistor. How many coulombs of charge will flow through the resistor in 90 seconds.

electrical energy coulomb flow

Electrical Energy: The Watt

Electrical Power is the product of the two quantities, Voltage and Current and so can be defined as the rate at which work is performed in expending energy. We said previously that voltage provides the work required in Joules to move one Coulomb of charge from A to B and that current is the rate of movement (or rate of flow) of the charge. So how are these two definitions linked together.

If voltage, (V) equals Joules per Coulombs (V = J/C) and Amperes (I) equals charge (coulombs) per second (A = Q/t), then we can define electrical power (P) as being the totality of these two quantities. This is because electrical power can also equal voltage times amperes, that is: P = V*I.

The Watt

electrical energy the watt

So we can see that electrical power is also the rate at which work is performed during one second. That is, one joule of energy dissipated in one second. As electrical power is measured in Watts (W), therefore it must be also be measured in Joules per Second. So we can correctly say that: 1 watt = 1 joule per second (J/s).

Electrical Power

So if 1 watt = 1 joule per second, it therefore follows that: 1 Joule of energy = 1 watt over one unit of time, that is: Work equals Power multiplied by Time, (V*I*t joules). So electrical energy (the work done) is obtained by multiplying power by the time in seconds that the charge (in the form of a current) flows. Thus units of electrical energy depend on the units used for electric power and time. So if we measure electrical power in kilowatts (kW), and the time in hours (h), then the electrical energy consumed equals kilowatts*hours (Wh) or simply: kilowatt-hours (kWh).

Electrical Energy Example No3

A 100 Watt light bulb is illuminated on for one hour only. How many joules of electrical energy have been used by the lamp.

joules of a light bulb

Note that when dealing with the joule as a unit of electrical energy, it is more convenient to present them in kilo-joules. Thus the answer can be given as: 360kJ. As a joule on its own is a small quantity, the kilojoule (kJ), thousands of joules, the megajoule (MJ), millions of joules, and even the gigajoule (GJ), thousands of millions of joules, are all practical units of electrical energy. Thus one unit of electricity which is one kilowatt-hour (kWh) is equivalent to 3.6 megajoules (MJ).

Likewise, since a Watt is such a small amount of electrical power, kilowatts (1 kW = 1,000 watts) and megawatts (1 MW = 1 million watts) are commonly used to identify the power output of electrical equipment and appliances. Thus we can see that the kilowatt (or megawatt) is a unit of electrical power, while the kilowatt-hour is a unit of electrical energy.

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