PANTOMATH

Posted: **Mon Nov 04, 2024 3:20 pm**

Power and Energy Concepts

Resistance: Ohm’s Law, Series and Parallel Circuits

Resistance

Resistance is a measure of how much a material or component opposes the flow of electric current through it. In simple terms, resistance limits or resists the movement of electrical charges (electrons) in a circuit.

Ohm’s Law:

Ohm’s Law is a fundamental principle in electrical circuits that states the relationship between voltage (V), current (I), and resistance (R). It is expressed as:

V=I×RV = I \times RV=I×R

Where:

I is the current (in amperes or amps)
R is the resistance (in ohms, denoted by Ω)
Voltage (V): The electric potential difference between two points, pushing electrons through a conductor, measured in volts (V).
Voltage in a Transformer:
- A transformer is an electrical device that changes the voltage of alternating current (AC) from one level to another, either increasing (step-up transformer) or decreasing (step-down transformer) the voltage, while maintaining the same frequency.
- Step-up Transformer: If Ns>Np ,the transformer increases the voltage.
- Step-down Transformer: If Ns<Np, the transformer decreases the voltage.

Voltage in an Adapter (AC to DC Adapter):

An adapter (also called a power adapter or charger) is a device that converts alternating current (AC) from a wall outlet to a lower voltage and changes it to direct current (DC) to power electronic devices.
For example, a phone charger might step down 220V AC to 5V DC, while a laptop adapter might step down to 19V DC. The exact output voltage depends on the requirements of the device the adapter is powering.

From this equation, you can also calculate:

I=V/R (current)
R=V/I (resistance)

Series Circuits:

In a series circuit, resistors (or other components) are connected end-to-end, meaning the same current flows through each resistor.

Parallel Circuits:

In a parallel circuit, resistors are connected across the same two points, so each has its own path for the current. The voltage across each resistor is the same, but the current splits among the resistors.

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Voltage: AC vs DC, Power Transmission

1. Voltage in DC (Direct Current):

In DC circuits, the voltage remains constant over time. The current flows in one direction only, meaning that there is a steady, unidirectional flow of electric charge.

Characteristics of DC Voltage:

Constant Voltage: The voltage in a DC system is fixed at a certain level and does not change its direction or magnitude. For example, a 12V DC battery provides a constant 12 volts as long as the battery is charged.
Direction: DC voltage always pushes current in a single direction through the circuit.
Source of DC Voltage: Common sources include batteries, solar panels, and DC power supplies. In these cases, devices are powered by a consistent voltage, ensuring stable operation for electronics.

Examples of DC voltage:

• A 9V battery has a constant voltage of 9 volts across its terminals.
• A USB port delivers a steady 5 volts DC to power devices.

2. Voltage in AC (Alternating Current):

In AC circuits, the voltage varies with time, regularly reversing its direction. The alternating nature of AC allows the voltage to rise and fall, changing polarity.

Characteristics of AC Voltage:

Varying Voltage: AC voltage oscillates between positive and negative values, following a sinusoidal waveform. This means the voltage periodically reverses its direction. In most countries, AC voltage follows a frequency of either 50 Hz or 60 Hz, meaning it changes direction 50 or 60 times per second.
Sinusoidal Waveform: AC voltage can be described by a sine wave, where the voltage smoothly transitions between its peak positive and peak negative values.
RMS Voltage: Since AC voltage fluctuates, we often refer to its RMS (Root Mean Square) value, which represents the equivalent DC voltage that would provide the same amount of power. The RMS voltage is lower than the peak voltage. For example:
- In the U.S., the standard household voltage is 120V RMS, but the peak voltage is about 170V.
- In many other countries, the standard is 230V RMS, with a peak voltage of about 325V.
Source of AC Voltage: AC voltage is generated by power plants and is used in homes and industries because it is more efficient to transmit over long distances.

Examples of AC voltage:

The wall socket in a home typically supplies 120V or 230V AC, depending on the country.
AC voltage is used for powering large appliances (refrigerators, washing machines) and general household lighting.

Power Transmission and Voltage

Power transmission is the process of transferring electrical power from generating stations (such as power plants) to homes, businesses, and industries through a network of transmission lines. Voltage plays a crucial role in the efficiency of power transmission over long distances.

Why High Voltage is Used in Power Transmission:

Efficiency in Long-Distance Transmission: Power is generated at relatively low voltages (in the range of 10 kV to 30 kV) at power plants but is stepped up to extremely high voltages (in the range of 110 kV to 765 kV or more) for transmission. This allows power to be transmitted over hundreds of kilometers with minimal losses.

Transformers and Voltage:
- Step-Up Transformers: At the power plant, step-up transformers increase the voltage for transmission. This reduces the current and minimizes losses.
- Step-Down Transformers: Near the consumption points (cities, towns, or factories), step-down transformers reduce the voltage to safer, usable levels (such as 230V or 120V for households) and increase the current to match the power requirements of the loads.

Reducing Power Losses: Power loss in transmission lines is proportional to I2I^2I2, so even a small reduction in current results in a significant reduction in losses. By transmitting at high voltages, the current can be reduced significantly, thus reducing the heat losses due to resistance in the wires.

Voltage Levels in Power Transmission:
- Low Voltage Distribution: After power has been transmitted across long distances, it is stepped down to lower voltages for distribution within neighborhoods or to individual homes. Common household voltages are 120V (in the U.S.) or 230V (in many other countries).
- High Voltage Transmission Lines: High-voltage transmission lines range from 110 kV (kilovolts) to 765 kV or more, depending on the distance and the amount of power being transmitted.

Windmill Technology: Components and Power Generation Process

Windmill technology harnesses the kinetic energy of wind to generate electrical power. Modern windmills, commonly referred to as wind turbines, convert wind energy into electrical energy using aerodynamic blades and sophisticated mechanical and electrical systems. Here’s an overview of the key components and the process of power generation in windmills.

Components of a Windmill (Wind Turbine):

1.Rotor Blades:

Function: The rotor blades capture the kinetic energy from the wind. Most modern wind turbines have three blades.
Design: The blades are shaped like an airplane wing (aerofoil shape) to generate lift as the wind flows over them. This lift causes the blades to spin.
Material: Typically made of composite materials (fiberglass, carbon fiber) for strength and lightness.

2.Nacelle:

Function: The nacelle is the housing that sits at the top of the tower, containing key mechanical and electrical components.
Contains:
- Gearbox: Increases the rotational speed of the blades to the required speed for electricity generation (most turbines increase rotation from ~30-60 RPM to around 1,000-1,500 RPM).
- Generator: Converts mechanical energy from the spinning rotor into electrical energy.
- Brake System: Stops the rotor in case of emergency or maintenance.

3.Tower:

Function: The tower supports the nacelle and rotor blades. It elevates the blades to a height where wind speeds are higher and more consistent.
Height: Towers range from 80 meters to over 150 meters in height, depending on the turbine size.
Material: Usually made of steel or reinforced concrete.

4.Hub:

Function: The hub connects the rotor blades to the turbine’s shaft, transmitting the mechanical energy from the rotating blades to the drivetrain.

5.Drivetrain:

Function: Transmits mechanical energy from the rotating blades to the generator. The gearbox is a critical part of this system.

6.Generator:

Function: Converts mechanical energy (rotational motion) into electrical energy.
Type: Typically an AC (alternating current) generator, often a synchronous or asynchronous type.

7.Yaw System:

Function: Rotates the nacelle horizontally to align the blades with the wind direction.
Yaw Motor: Adjusts the orientation of the nacelle to capture the maximum wind energy.

8.Anemometer and Wind Vane:

Anemometer: Measures wind speed.
Wind Vane: Measures wind direction.
Function: These instruments provide data to control systems that adjust the yaw and blade pitch for optimal performance.

9.Controller:

Function: The controller monitors the system’s performance, including wind speed and direction, and ensures the turbine operates within safe parameters. It also starts or stops the turbine depending on conditions.

10.Pitch System:

Function: Adjusts the angle (pitch) of the rotor blades to control the turbine’s rotational speed and efficiency. In high winds, the pitch system reduces the angle of the blades to prevent damage.

11.Foundation:

Function: Anchors the tower to the ground, ensuring stability.
Material: Usually made of concrete and reinforced with steel.

Power Generation Process in Wind Turbines:

1.Wind Energy Capture:

Wind flows over the rotor blades, creating lift due to their aerofoil shape. The blades spin as a result, and the rotor converts the wind’s kinetic energy into mechanical energy.

2.Rotor Rotation:

As the rotor spins, the energy is transferred to the hub and through the shaft to the gearbox. The rotor’s slow rotation (typically 30-60 revolutions per minute) is too slow for efficient electricity generation, so the gearbox increases the speed to the desired level (usually around 1,000-1,500 RPM).

3.Generator Operation:

The high-speed rotation is passed to the generator, which converts the mechanical energy into electrical energy. Most wind turbines use an AC generator that produces alternating current, though DC systems can be used in smaller turbines.
How the generator works: Inside the generator, a magnetic field induces electrical current as the rotor spins. This is based on Faraday’s law of electromagnetic induction.

4.Electricity Transmission:

The generated electricity is often at a relatively low voltage. A step-up transformer located either in the nacelle or at the turbine base increases the voltage to a higher level suitable for transmission over long distances. This reduces transmission losses.
The electricity is then sent through cables down the tower to the ground station, where it is transmitted to the grid.

5.Grid Integration:

Once the power has been generated, it is transmitted to a local substation and integrated into the electricity grid, where it can be distributed to homes, businesses, and industries.