ENERGY, POWER AND RESISTANCE

1. Circuit symbols:

• a) Circuit symbols:
• In electrical and electronic diagrams, circuit symbols are crucial for standardizing and simplifying the representation of intricate circuits and components.
• For engineers, electricians, and technicians to comprehend circuit operations without documentation, these symbols are essential.
• These symbols’ universal acceptance guarantees consistent interpretation across languages and geographical areas, supporting training and education.

Circuit Name	Circuit and symbol
Transistor
Diode
LED
Photodiode
Integrated circuit
Operational amplifier
Seven segment display
Battery
Resistance
Thermistor
Capacitor
Transformer

• b) Circuit diagrams using these symbols:
• Here’s a brief explanation of each component and a simple circuit diagram using each symbol:

2. E.m.f. and p.d:

• a) Potential difference (p.d); the unit volt:
• Potential difference (p.d) is another term for voltage, which is the measure of the electric potential energy per unit charge between two points in a circuit. The unit of measurement for voltage is the volt (V).
• In other words, voltage is the “pressure” that drives electric current through a circuit. The higher the voltage, the greater the electric potential energy per unit charge.
• About voltage:
• – Symbol: V (for voltage) or U (in some European countries)
• – Unit: Volt (V)
• – Measured with: Voltmeter
• – Formula:
• [math]V = I \times R \quad \text{(Ohm’s Law)}[/math]
•  Where V is voltage, I is current, and R is resistance
• Some common voltage values include:
• – Household power outlets: 120V (US) or 230V (Europe)
• – Batteries: 1.5V (AA), 9V (transistor), 12V (car)
• – Electronic devices: 3.3V, 5V (USB), 12V (computer)
• b) Electromotive force (e.m.f) of a source such as a cell or a power supply:
• Electromotive force (e.m.f) is the energy provided by a source, such as a cell or power supply, to drive electric charge through a circuit. It’s the “push” that causes electrons to flow. e.m.f is measured in volts (V) and is often denoted by the symbol ε (epsilon).
• – Symbol: ε (epsilon)
• – Unit: Volt (V)
• – Definition: Energy per unit charge provided by a source
• – Formula:
• [math]\varepsilon = V \, (\text{voltage}) = I \, (\text{current}) \times R \, (\text{resistance})[/math]
• e.m.f is the potential difference between the terminals of a source when no current is flowing. It’s the maximum voltage that the source can provide.
• For example:
• – A battery has an e.m.f of 1.5V
• – A power supply has an e.m.f of 12V
• e.m.f is not the same as voltage, although they are related. Voltage is the potential difference between two points in a circuit, while e.m.f is the energy provided by a source.
• c) Distinction between e.m.f. and p.d in terms of energy transfer:
• The distinction between e.m.f. (electromotive force) and p.d. (potential difference) in terms of energy transfer is:
• Electromotive force (e.m.f). (ε):
• – Energy provided by a source (e.g., battery, power supply)
• – Measures the energy per unit charge supplied by the source
• – Responsible for “pushing” electric charge through a circuit
• – Associated with the work done to move a charge between the terminals of a source
• – Formula:
• [math] \text{p.d} = \frac{\text{Work done}}{\text{Charge}}[/math]
• Potential difference (p.d). (V):
• – Energy required to move a charge between two points in a circuit
• – Measures the energy per unit charge expended in moving charge between two points
• – Responsible for the “flow” of electric charge in a circuit
• – Associated with the work done to move a charge through a circuit element (e.g., resistor)
• – Formula:
• [math]\text{p.d} = \frac{\text{Work done}}{\text{Charge}}[/math]
• 
• Figure 1 Difference between e.m.f and p.d
• In other words:
• – e.m.f. is the energy provided by a source, while p.d. is the energy expended in a circuit.
• – e.m.f. is the “pressure” that drives electric charge, while p.d. is the “drop” in energy as charge flows through a circuit.
• To illustrate the difference:
• – A battery has an e.m.f. of 1.5V, meaning it provides 1.5 joules of energy per coulomb of charge.
• – A resistor in a circuit has a p.d. of 1.5V, meaning 1.5 joules of energy are expended to move a coulomb of charge through the resistor.
• e.m.f. is the energy source that drives electric charge.
• p.d. is the energy expended as charge flows through a circuit.
• d) Energy transfer;[math]W = VQ; \quad W = \varepsilon Q[/math]
• The e.m.f is supply such as a solar cell is the energy transferred (W) by the supply when charge Q passes through the cell
• [math]\varepsilon = \frac{\text{Energy transferred to charge}}{\text{Charge}}[/math]
• [math]\varepsilon = \frac{W}{Q}[/math]
• [math]W = Q \varepsilon[/math]
• Since the unit of energy is joule and the unit of charge is coulomb, the S.I. unit of e.m.f. is joules per coulomb, also known as volts (V).
• [math]1 \, \text{J} \, \text{C}^{-1} = 1 \, \text{V}[/math]
• The p.d. ( V ) across a component is the energy transferred to the component (the work done) when charge Q passes through it .
• [math]\text{p.d} = \frac{\text{Energy transferred to charge}}{\text{Charge}}[/math]
• [math]V = \frac{W}{Q}[/math]
• The unit of p.d is also [math]1 \, \text{J} \, \text{C}^{-1} \, \text{or} \, 1 \, \text{V}[/math] .
• e) Energy transfer;[math]eV = \frac{1}{2} m v^2[/math] for electrons and other charged particles:
• The charge carriers are electrons. A dynamo, battery or solar cell transfers energy to each electron that passes through.
• Each electron has a charge of e coulombs, so an energy change of eV takes place when an electron passes through a p.d. V.
• The energy transferred when one electron travels through a potential difference of one volt is a derived unit called one electron volt.
• When a potential difference is applied across a conductor, the electrons are accelerated and gain kinetic energy. When an electron is accelerated through a p.d. V, the kinetic energy gained is:
• [math]eV = \frac{1}{2} m v^2[/math]
• – e: elementary charge (approximately [math]1.6 \times 10^{-19}[/math] Coulombs)
• – V: voltage (potential difference)
• – m: mass of the charged particle (e.g., electron)
• – v: velocity of the charged particle
• This equation states that the energy (eV) of a charged particle is equal to the kinetic energy ([math]\frac{1}{2} m v^2[/math]) of the particle.
• The energy of a charged particle is directly proportional to its mass and the square of its velocity.
• For electrons and other charged particles, this equation helps us understand how their energy changes as they move through electric fields or are accelerated by voltages.

3. Resistance:

• a) Resistance;[math]R = \frac{V}{I}[/math]  the unit ohm:
• Resistance (R) is the opposition to the flow of electric current (I) through a conductor, such as a wire. It depends on the material, shape, and size of the conductor.
• Resistance converts some of the energy carried by the current into heat, so it can be thought of as the “friction” that slows down electric charge as it flows through a conductor.
• [math]R = \frac{V}{I}[/math]
• This equation defines resistance (R) as the ratio of voltage (V) to current (I).
• Resistance is the opposition to the flow of electric current.
• It depends on the material, shape, and size of the conductor.
• The unit of resistance is the ohm (Ω), named after Georg Ohm, who discovered the relationship between voltage, current, and resistance.
• – Resistance is a scalar quantity, meaning it has only magnitude (amount) but no direction.
• – The ohm (Ω) is defined as 1 volt per ampere (1 V/A).
• – Resistance can be thought of as the “friction” that slows down electric charge as it flows through a conductor.
• b) Ohm’s law:
• Ohm’s Law states that the current (I) flowing through a conductor is directly proportional to the voltage (V) applied across it, and inversely proportional to the resistance (R) of the conductor.
• Mathematically, Ohm’s Law is expressed as:
• [math]I = \frac{V}{R}[/math]
• Where:
• – I is the current in amperes (A)
• – V is the voltage in volts (V)
• – R is the resistance in ohms (Ω)
• This fundamental law describes the relationship between voltage, current, and resistance, and is a cornerstone of electric circuit analysis.
• – The law assumes a linear relationship between voltage and current.
• – Resistance is constant, independent of voltage and current.
• – The law applies to any conductor, including wires, resistors, and other components.
• You can use a circuit that has a variable number of cells connected to a long length of thin wire (Figure 2) to repeat Ohm’s experiment using modern instruments.
• Include an ammeter in the circuit to measure the current, and a voltmeter to measure potential difference.
• Using a long length of thin wire and a switch keeps the current at a low value so the heating effect is negligible.
• 
• Figure 2 A circuit which can measure voltage, current, and resistance by suing Ohm’s Law

• c) i) characteristics of resistor, filament lamp, thermistor, diode and light-emitting diode (LED):
• ⇒ The I-V graph of a resistor:
• The I-V graph of a resistor is a straight line that shows the relationship between current (I) and voltage (V) across the resistor. Here are the characteristics of an I-V graph for a resistor:
• – Linear: The graph is a straight line, indicating a linear relationship between current and voltage.
• – Passing through the origin: The graph passes through the origin (0, 0), meaning that if there is no voltage applied, there is no current flowing.
• 
• Figure 3  characteristic graph of resistance
• – Positive slope: The slope of the line is positive, indicating that current increases as voltage increases.
• – Constant resistance: The slope of the line represents the resistance (R) of the resistor, which is constant.
• – No saturation: The graph does not show any saturation or limiting of current, as resistors do not have a maximum current rating.
• – Ohm’s Law: The graph illustrates Ohm’s Law, I = V/R, where the slope of the line represents the resistance (R).
• The I-V graph of a resistor is a straight line only if the resistor is ideal and operates within its specified temperature range.
• Real-world resistors may exhibit non-linear behavior due to various factors, such as temperature changes or material properties.
•  The I-V graph of a resistor can be used to determine its resistance value by measuring the slope of the line.
• ⇒ The I-V graph of a filament lamp:
• The I-V graph of a filament lamp is different from a resistor’s graph. Here’s what you’d observe:
• – Non-linear: The graph is curved, indicating a non-linear relationship between current and voltage.
• – Positive slope: The slope of the curve is positive, meaning current increases as voltage increases.
• – Saturation: The graph shows saturation, meaning that beyond a certain voltage, the current does not increase significantly. This is due to the filament’s limited temperature and the resulting decrease in resistance.
• – Negative resistance region: The graph may exhibit a negative resistance region, where the current decreases with increasing voltage. This is caused by the filament’s thermal characteristics.
• – Hysteresis: The graph may show hysteresis, meaning that the curve is different when the voltage is increasing versus decreasing. This is due to the filament’s thermal inertia.
• – Non-ohmic: The graph does not follow Ohm’s Law, as the filament’s resistance changes with temperature and voltage.
• 
• Figure 4 (a) The I-V graph of a filament lamp (b) Initially, as the potential difference across the fi lament lamp increases, the current increases in an almost linear way. At higher potential differences, the gradient decreases as the current increases. A fi lament lamp is a non-ohmic conductor
• The I-V graph of a filament lamp is a result of the complex relationship between the filament’s temperature, resistance, and the applied voltage. This non-linear behavior is why filament lamps are often driven with a current-limiting device, like a resistor, to prevent overheating and prolong their lifespan.
• ⇒ The I-V graph of a diode or LED:
• Reversing the direction of the e.m.f. in a simple circuit causes the current to reverse through a resistor or fi lament lamp.
• With a diode this is not the case: the diode will allow current to flow through it in only one direction, from positive to negative. This is called the forward bias direction.
• In the reverse bias direction, effectively no current can pass and the diode is said to have almost infinite resistance.
• This can be seen in Figure 5 reversing the cell polarity leads to no current, regardless of how high the e.m.f.
• 
• Figure 5 (a) Investigating the behavior of a diode (b) The I– V behavior of a diode
• Diodes are simple devices that allow an electric current to pass in only one direction.
• Through developments in technology, their usefulness has increased. The current passing through them can now be much larger and some types, called light-emitting diodes (LEDs), emit visible light when current flows through them.
• You can buy LEDs that act as strong sources of white light or any other color.
• – Switch on instantly
• – Very robust
• – Very versatile
• – Operate with low potentials
• – Long working life.
• They are increasingly being used as light sources, and high-powered LEDs are expected to transform electric lighting.
• 10 000 LEDs can be used in a set of traffic lights compared with a single LED in the on/off indicator of a TV set.
• The I-V graph of a Thermistor:
• The I-V graph of a thermistor (temperature-sensitive resistor) exhibits some unique characteristics:
• 
  Figure 6 The resistance of a negative coefficient thermistor decreases as its temperature increases,
• – Non-linear: The graph is curved, showing a non-linear relationship between current and voltage.
• – Negative slope: The slope of the curve is negative, meaning current decreases as voltage increases.
• – Temperature-dependent: The graph changes significantly with temperature. As temperature increases, the curve shifts downward, indicating decreased resistance.
• – Resistance decreases with temperature: The graph shows that resistance decreases as temperature increases, which is the opposite of a typical resistor.
• – Non-ohmic: The graph does not follow Ohm’s Law, as the thermistor’s resistance changes significantly with temperature.
• – Steep curve: The graph has a steep curve, indicating a large change in current for a small change in voltage.
• Thermistors are used in temperature measurement and control applications due to their high sensitivity and rapid response to temperature changes. The I-V graph of a thermistor is a key characteristic used in designing and analyzing thermistor circuits.
• ⇒ Techniques and procedures used to investigate the electrical characteristics for a range of ohmic and non-ohmic components.
• To investigate the electrical characteristics of ohmic and non-ohmic components, the following techniques and procedures can be used:
• Ohmic Components:
• – Measure resistance using a multimeter
• – Use a variable power supply to apply different voltages
• – Measure current using an ammeter
• – Plot I-V graphs to demonstrate ohmic behavior
• – Calculate resistance using Ohm’s Law ([math]R = \frac{V}{I}[/math])
• Non-Ohmic Components:
• – Measure current-voltage characteristics using a curve tracer or oscilloscope
• – Use a function generator to apply different waveforms
• – Measure voltage and current using a multimeter or oscilloscope
• – Plot I-V graphs to demonstrate non-ohmic behavior
• – Analyze the graph to determine the type of non-ohmic component (e.g., diode, transistor)
• Additional Techniques:
• – Sweep testing: Vary the voltage and measure the resulting current
• – Step testing: Apply a fixed voltage and measure the resulting current
• – Pulse testing: Apply a brief pulse and measure the response
• – Frequency response analysis: Measure the component’s response to different frequencies
• – Load line analysis: Plot the component’s I-V graph with a load line to determine operating points
• Procedures:
• – Ensure proper instrumentation and measurement setup
• – Follow safety protocols when working with electrical components
• – Take multiple measurements to ensure accuracy
• – Use appropriate units and scaling when plotting graphs
• – Analyze and interpret the data to draw conclusions about the component’s electrical characteristics
• By using these techniques and procedures, you can investigate the electrical characteristics of various ohmic and non-ohmic components, gaining a deeper understanding of their behavior and properties.
• ⇒ Light-dependent resistor (LDR):
• A Light-Dependent Resistor (LDR) is a type of resistor that changes its resistance in response to changes in light levels. It is also known as a photoresistor or photocell.
• Characteristics of LDR:
• – Resistance decreases as light intensity increases
• – Resistance increases as light intensity decreases
• – Sensitive to visible and infrared light
• – Can be used to detect light levels, motion, and proximity
• – Commonly used in:
• Light sensing applications (e.g., automatic lighting systems)
• Security systems (e.g., motion detectors)
• Camera lenses (e.g., aperture control)
• Solar panels (e.g., maximum power point tracking)
• Types of LDR:
• – Cadmium Sulfide (CdS) LDR: most common type, sensitive to visible light
• – Cadmium Selenide (CdSe) LDR: more sensitive than CdS, used in applications requiring higher sensitivity
• – Infrared (IR) LDR: sensitive to infrared light, used in applications such as motion detection
• 
• Figure 7 LDR with I-V characteristic graph
• How LDR works:
• – Light hits the LDR, exciting electrons and allowing them to flow more freely
• – Increased electron flow reduces resistance
• – Resistance change is proportional to light intensity
• By using an LDR, you can create innovative projects that interact with light, such as automatic night lights, solar-powered chargers, or even a light-controlled robot.

4. Resistivity:

• a) i) Resistivity of a material; the equation [math]R = \frac{\rho L}{A}[/math]:
• The resistivity of a material (ρ) is a fundamental property that determines how much a material resists the flow of electric current.
• In algebraic form this gives “resistance is directly proportional to the length of the wire”.
• [math]R \propto L[/math]
• “Also, the resistance of the material is inversely proportional to the cross-sectional area of that material wire which possessing through the current”.
• [math]R \propto \frac{1}{A}[/math]
• Combining these equations then
  
• [math]R \propto \frac{L}{A}[/math]
• [math]R = \frac{\rho L}{A}[/math]
• This equation relates the resistivity of a material to the resistance (R) of a conductor with length (L) and cross-sectional area (A).
• – R (resistance): the opposition to the flow of electric current
• – ρ (resistivity): the material’s property that determines its resistance (measured in ohm-meters, Ωm)
• – L (length): the length of the conductor (measured in meters, m)
• – A (cross-sectional area): the area of the conductor’s cross-section (measured in square meters, m²)
• The equation shows that:
• – Resistance increases with length (L) and resistivity (ρ)
• – Resistance decreases with increasing cross-sectional area (A)
• Resistivity (ρ) is a material constant that depends on the material’s properties, such as temperature, composition, and crystal structure. Some materials have high resistivity (e.g., wood, rubber), while others have low resistivity (e.g., copper, aluminum).
• This equation is essential in designing and analyzing electric circuits, as it helps you calculate the resistance of a conductor and understand how it affects the flow of electric current.
• Table 1 Resistivities of different materials at 20 °C

• ii)Techniques and procedures used to determine the resistivity of a metal:
• To determine the resistivity of a metal, the following techniques and procedures can be used:
• – Four-Probe Method: Uses a device with four probes to measure the voltage and current across a metal sample.
• – Two-Probe Method: Similar to the four-probe method but uses only two probes.
• – Resistivity Measurement System: Commercial systems that use a combination of probes and electronics to measure resistivity.
• – Ohm’s Law Method: Measures the voltage and current across a metal sample and calculates resistivity using Ohm’s Law([math]R = \frac{V}{I}[/math]) .
• – Van der Pauw Method: A technique used for measuring resistivity and hall coefficient of a material.
• – Eddy Current Method: Non-destructive testing method that uses electromagnetic induction to measure resistivity.
• – Contactless Resistance Measurement: Uses a magnetic field to measure resistivity without physical contact.
• Procedures:
• – Prepare a metal sample with uniform cross-sectional area and length.
• – Measure the length and cross-sectional area of the sample.
• – Set up the measurement device or system.
• – Apply a current or voltage across the sample.
• – Measure the resulting voltage or current.
• – Calculate resistivity using the measured values and the equation[math]R = \frac{\rho L}{A}[/math]
• – Repeat measurements at different temperatures or conditions as needed.
• Semiconductors:
• – Resistivity decreases with temperature (negative temperature coefficient)
• – As temperature rises, more electrons are excited into the conduction band, increasing conductivity
• – At high temperatures, resistivity may increase due to thermal generation of charge carriers.
• Temperature ranges:
• – Metals: Linear increase in resistivity with temperature (0-100°C)
• – Semiconductors: Exponential decrease in resistivity with temperature (0-100°C), then linear increase at high temperatures
• b) Negative temperature coefficient (NTC) thermistor; variation of resistance with temperature.
• A Negative Temperature Coefficient (NTC) thermistor is a type of thermistor that exhibits a decrease in resistance as the temperature increases. The variation of resistance with temperature is typically exponential in nature.
• Characteristics of NTC thermistors:
• – Resistance decreases with increasing temperature
• – High sensitivity to temperature changes
• – Fast response time
• – Non-linear resistance-temperature relationship
• – Typically made from metal oxides (e.g., nickel, manganese, cobalt)
• The resistance-temperature relationship of an NTC thermistor can be described by the following equation:
• [math]R = R_0 \exp\left(-B\left(\frac{1}{T} – \frac{1}{T_0}\right)\right)[/math]
• Where:
• R = resistance at temperature T
• [math]R_0[/math]= resistance at reference temperature T0
• B = thermistor constant
• T = temperature in Kelvin
• [math]T_0[/math]= reference temperature in Kelvin
• NTC thermistors are commonly used in:
• – Temperature measurement and control
• – Thermal protection and sensing
• – Automotive applications
• – Medical devices
• – Industrial automation
• The advantages of NTC thermistors include:
• – High accuracy
• – Fast response time
• – Small size
• – Low cost
• – Easy integration into circuits
• However, NTC thermistors also have some limitations:
• – Non-linear resistance-temperature relationship
• – Limited operating temperature range
• – Sensitive to environmental factors (e.g., humidity, pressure)
• Overall, NTC thermistors are a popular choice for temperature measurement and control applications due to their high sensitivity, fast response time, and small size.

5. Power:

• a) Power:
• Power, in the context of electronics and electrical engineering, refers to the rate at which electrical energy is transferred or converted. It is typically measured in units of watts (W).
• Power can be calculated using the following formulas:
• [math]P \, (\text{Power}) = V \times I \, (\text{Voltage} \times \text{Current})[/math]
• [math]P \, (\text{Power}) = \frac{V^2}{R} \, (\text{Voltage}^2 / \text{Resistance})[/math]
• [math]P = I^2 R \, (\text{Power} = \text{Current}^2 \times \text{Resistance})[/math]
• Where:
• – P is the power in watts (W)
• – V is the voltage in volts (V)
• – I is the current in amperes (A)
• – R is the resistance in ohms (Ω)
• There are different types of power, including:
• – Active power (P): The actual power consumed or produced by a device.
• – Reactive power (Q): The power stored or released by a device due to inductive or capacitive loads.
• – Apparent power (S): The vector sum of active and reactive power.
• Power is a fundamental concept in electronics and electrical engineering, and understanding it is crucial for designing and analyzing electrical circuits and systems.
• Examples:
• A nuclear power station transfers [math][/math] of energy from nuclear energy to electrical energy in a one hour period.
• Calculate:
• (a) the power of the nuclear power station in watts
• (b) the current in the wires when the transmission voltage is 200 kV
• (c) the current in the wires when the transmission voltage is 2 kV
• (d) the ratio power ‘wasted’ as heat at 2 kV: power ‘wasted’ as heat at 200 kV.
• Given data:
• Energy of the nuclear power station = E =[math]5.2 \times 10^{12} \, \text{J}[/math]
• Time = 1h = 3600s
• Transmission voltage = V = 200 kV =[math]200 \times 10^3 \, \text{V}[/math]
• Wasted voltage as a heat = V = 2 kV = 2000 V
• Power wasted as a heat = 200 kV =[math]200 \times 10^3 \, \text{V}[/math]
• Find data:
• Power = P =?
• Current in wire at 200 kV voltage = V =?
• Current in wire at 2 kV voltage = V =?
• The ratio power ‘wasted’ as heat at 2 kV: power ‘wasted’ as heat at 200 kV = P =?
• Formula:
• [math]P = \frac{E}{t} \\
  I = \frac{P}{V} \\
  P = I^2 R[/math]
• Solution:
• a).
• [math]P = \frac{E}{t} \\
  P = \frac{5.2 \times 10^{12}}{3600} \\
  P = 1.4 \times 10^9 \, \text{W}[/math]
• b).
• [math]I = \frac{P}{V} \\
  I = \frac{1.4 \times 10^9}{200 \times 10^3} \\
  I = 7000 \, \text{A}[/math]
• c).
• [math]I = \frac{P}{V} \\
  I = \frac{1.4 \times 10^9}{2000} \\
  I = 700,000 \, \text{A}[/math]
• d).
• [math]P = I^2 R \\
  P = (700,000)^2:{(7000)^2} \\
  P = 10,000:{1}[/math]
• This means that 10 000 times more heat will be ‘wasted’ when the current is increased by a factor of 100.
• e) Energy transfer; W = VIt
• Energy transfer is the process by which energy is moved from one location to another or transformed from one form to another. In the context of electronics and electrical engineering, energy transfer refers to the transfer of electrical energy from one circuit element to another or from one system to another.
• Types of energy transfer:
• – Electrical energy transfer: Transfer of energy through electrical currents and voltages.
• – Electromagnetic energy transfer: Transfer of energy through electromagnetic waves (e.g., light, radio waves).
• – Thermal energy transfer: Transfer of energy through temperature differences (e.g., heat transfer).
• – Mechanical energy transfer: Transfer of energy through mechanical movements (e.g., rotational, translational).
• W = VIt
• The equation represents the energy transfer in a circuit, where:
• – W is the energy transferred (measured in joules, J)
• – V is the voltage (measured in volts, V)
• – I is the current (measured in amperes, A)
• – t is the time (measured in seconds, s)
• This equation states that the energy transferred is equal to the product of the voltage, current, and time. This is a fundamental concept in electronics and electrical engineering, as it describes the energy transfer in a circuit.
• In other words, the equation W = VIt
• shows that:
• – Energy (W) is transferred when a voltage (V) is applied across a conductor, causing a current (I) to flow for a certain time (t).
• – The amount of energy transferred is directly proportional to the voltage, current, and time.
• Methods of energy transfer:
• – Conduction: Direct transfer of energy between particles or objects in physical contact.
• – Convection: Transfer of energy through fluid motion (e.g., air, water).
• – Radiation: Transfer of energy through electromagnetic waves.
• – Induction: Transfer of energy through magnetic fields.
• – Capacitance: Transfer of energy through electric fields.
• Efficiency of energy transfer:
• The efficiency of energy transfer depends on various factors, such as:
• – Resistance in the circuit
• – Quality of the energy source
• – Design of the energy transfer system
• – Environmental conditions (e.g., temperature, humidity)
• Understanding energy transfer is crucial in designing and optimizing electronic systems, ensuring efficient energy use, and minimizing energy losses.
• f) The kilowatt-hour (kW h) as a unit of energy; calculating the cost of energy:
• The kilowatt-hour (kW h) is a unit of energy that represents the amount of energy consumed or produced by a device or system over a period of time. It is defined as the energy consumed by a 1-kilowatt device operating for 1 hour.
• Calculating the cost of energy:
• To calculate the cost of energy, you need to know the following:
• – The amount of energy consumed (in kW h)
• – The cost of energy per unit (in $/kW h)
• The formula to calculate the cost of energy is:
• [math]\text{Cost} = \text{Energy consumption} \, (\text{kW} \cdot \text{h}) \times \text{Cost per unit} \, (\$/\text{kW} \cdot \text{h})[/math]
• For example:
• – Energy consumption: 500 kW h
• – Cost per unit: $0.15/kW h
• – Cost = 500 kW h x $0.15/kW h = $75
• So, the cost of energy in this example would be $75.
• Applications:
• – Measuring household energy consumption
• – Calculating electricity bills
• – Evaluating energy efficiency of devices and systems
• – Determining the cost-effectiveness of energy-saving measures
• Remember, kW h is a unit of energy, while kW (kilowatt) is a unit of power. Understanding the difference is crucial for accurate energy calculations.