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Electric Power

Power Generation

Electrical power may be generated by various means:

- Generator: electrical energy generated by the interaction of a magnetic field and an electric field. There is a mechanical rotation of a shaft (rotor) inside or outside a static part (stator). Either of the rotor or stator has a series of powerful magnets, and the other a dense series of conducting coils. The rotation of one inside the other generates an electromotive force (emf) by the interaction of the changing magnetic flux with the electric field of the electrons in the wires. Due to the rotation feature of the turbines, power generators are used to produce alternating current (AC), with a sinusoidal waveform.

- Thermocouple: exploiting the Seebeck Effect (thermoelectric principle). When two conductors of dissimilar (showing different properties) materials are brought into contact, there is an electrical current generated related to the difference in temperatures. Thermocouples are used to generate current, and for the operation of temperature sensors.

- Photosurface: in photovoltaic solar panels electricity may be generated by the quantum escapement of electrons from the surfaces of semi-conductors due to excitation by light radiation.

Electric power and energy.

$$P = VI$$

where P is the power needed to generate current I across a voltage difference V.

An electric motor is a device which provides mechanical force as a torgue on a shaft, by an electric current in a coil creating an electric field which provides force within a magnetic field.

$$E = F/q$$

It is the opposite of the generation of electrical current in the conversion of mechanical energy to electrical energy in a power generating plant.

Energy

When electrons start to travel around a circuit, there is a conversion of energy from the chemical energy of the battery to electrical energy. This energy is used to 'push' the electrons through loads.

For example, the electrons may excite the filament of a lamp or a kettle to glow and give out heat and light. Or they might drive a motor, or sound a buzzer.

Electrical energy E is the power P times the time t the power is applied for:

$$E = Pt$$

The unit of electrical energy is joule (J).

Power

Electrical power P is the voltage V times the current I:

$$P = IV$$

The unit of electrical power is watt (W), and is equivalent to $1 J/s$, one joule of energy per second.

A kilowatt (kW) is the power level which consumes 1 kJ (one thousand joules). A kW-s is the power that consumes 1 kJ in one second. A kWh is therefore the power that consumes 3600 joules in one hour. (There are 3600 seconds in one hour)

Example

Ammeter and voltmeter in a circuit
Ammeter and voltmeter in a circuit

In the photograph, it can be seen that LEDs are being powered by a power supply. The current is 49 mA, and the voltage is 5V.

The power P used to light the LEDs is:

$$P = IV = 49 x 10^{-3} ⋅ 5 $$ $$= 0.245 W$$

Question: if the LEDs are left on for one hour (3600 s), how much energy would be consumed?

The energy consumed is:

$$E = Pt = 0.245 ⋅ 3600 $$ $$= 882 J$$

Power Dissipation

When power is used to push electrons through a resistor, we say the power is 'dissipated'. This is another way of saying that the energy the power is supplying is being converted to heat, light or mechanical energy, and lost from the electrical energy of the circuit.

Since Ohm's Law tells us that $V = IR$, we can add this to the power equation $P = IV$ to get:

$$P = IV = I⋅IR = I^2R$$

Example

How much more power is dissipated in a resistor if the current is doubled?

Let $I_1$ be the first case, and $I_2$ the second. R is the same in both cases.

$$P_1 = I_1^2R$$ $$P_2 = I_2^2R$$

Since $I_2 = 2I_1$,

$$P_2 = (2I_1)^2R = 4I_1^2R = 4P_1$$

To double the current, four times as much power must be dissipated!

The reason for this is that the resistance of a load makes it hard to increase the current, so it is not linear.

Demonstration of the electric motor principle. A cork with a copper wire wrapped tightly around it, on a brass rod, suspended between two flat magnets.

Combined Cycle Electricity Generation

In the Carnot Engine, the greater the temperature differential between the input and output of a process, the greater the energy conversion possible.

Carnot heat engine
The Carnot heat engine explains why all energy conversions are inefficient

Fuel is burnt in a boiler, which is enveloped in tubes containing water. This water converts to steam, and under pressure of gas expansion can provide kinetic energy to drive a turbine. This turbine has a shaft which rotates, allowing electricity to be generated by the magnetic flux through coils of wire in the electrical generator. The amount of electricity generated depends on the energy provided by the steam to the turbine, since the mass of magnets or wire coils (either may rotate, while the other is static) must push against the electromagnetic resistance.

In a traditional single-cycle steam turbine, the steam returns to the water state, through cooling. This results in the loss of the residual heat in the water.

A combined cycle plant would incorporate a second cycle to exploit this latent heat, and can raise the efficiency of the overall electricity generation from 40 to 60%.

Content © Andrew Bone. All rights reserved. Created : April 7, 2014 Last updated :February 27, 2016

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