Current electricity

ELECTRICITY AQA A LEVEL PHYSICS

1. Understand Ohm’s Law in Electricity AQA A Level Physics: Grasp the relationship between voltage, current, and resistance.
2. Explore Series and Parallel Circuits in Electricity AQA A Level Physics: Learn how different configurations affect overall resistance and current flow.
3. Analyze Power Calculations for Electricity AQA A Level Physics: Master the formulas for calculating electrical power and energy consumption.
4. Examine Kirchhoff’s Laws in Electricity AQA A Level Physics:Apply these principles to solve complex circuit problems.
5. Study Electrical Components in Electricity AQA A Level Physics:Familiarize yourself with resistors, capacitors, and inductors, and their functions.
6. Understand Electromotive Force (EMF) in Electricity AQA A Level Physics: Learn how sources of EMF impact circuit behavior.
7. Investigate Practical Applications of Electricity AQA A Level Physics:See how electricity concepts apply in real-world scenarios and technology.

1. Moving charge and electric current:

• Moving charges are a fundamental concept in physics, especially in the study of electromagnetism.
• A moving charge is a charge that is in motion, like a proton or electron moving through space.
• When a charge moves, it creates a magnetic field around itself, which can interact with other charges and magnetic fields.
  – They create a magnetic field, which can be calculated using the Biot-Savart law or the Lorentz force equation.
  – The magnetic field generated by a moving charge depends on its velocity, direction, and the charge’s magnitude.
  – Moving charges can experience a force due to the magnetic field they generate, known as the self-force.
  – The concept of moving charges is crucial in understanding various phenomena, such as electric currents, electromagnetic induction, and particle accelerators.
• Electric current is the flow of electric charge, typically in the form of electrons moving through a conductor, such as a wire.
• [math] \text{Electric current } I \, (\text{A}) = \frac{\text{amount of charge flowing, } \Delta Q \, (\text{C})}{\text{time to flow, } \Delta t \, (\text{s})} \\ I \, (\text{A}) = \frac{\Delta Q \, (\text{C})}{\Delta t \, (\text{s})} [/math]
• – Electric current is the rate of flow of electric charge, typically measured in SI unit amperes (A).
  – It’s the movement of electrons from a negative terminal to a positive terminal, driven by a potential difference (voltage).
• There are two types of electric current:
  – Direct Current (DC): Flows in one direction only, like in a battery or electronic device.
  – Alternating Current (AC): Periodically reverses direction, like in a household power supply.
  – Resistance, impedance, and capacitance can affect electric current in a circuit.
• Many microelectronic circuits, like the printed circuit boards inside many computer systems, function with currents of the order of microamps (μA, 10⁻⁶ A), whereas electronic circuits, like those that control home appliances, often operate with considerably lower currents, milliamps (mA, 10⁻³ A).

  
  Figure 1 4 Electric currents can also
  be due to the flow of ions

• An electrolyte is a substance that helps conduct electricity in a solution, such as a liquid or a gel.
• Electrolytes are essential for various biological and chemical processes.
• Electrolytes are substances that dissolve in water or other polar solvents to produce ions, which can conduct electricity.
• Positive ions (cations) move toward the negative electrode
• Negative ions (anions) move towards the positive electrode.
• Electrons flow in the external circuit from the positive electrode to the negative electrode.

⇒ Example

If a car battery delivers 450 A for 2.5 seconds, calculate the total charge flowing, ∆Q.

• Given data:
  Time = t = 2.5 s
  Current = I =   450 A
• Find data:
  Flow of charges = ∆Q =  ?
• Formula:
• [math] \Delta Q = I * \Delta t [/math]
• Solution:
• [math] \Delta Q = I * \Delta t [/math]
• Put values
• [math] \Delta Q =450 * 2.5 \\ \Delta Q = 1125C[/math]

⇒ Variations of current with time:

• The fluctuation of the current taken from a cell over time is seen in Figure 5.
• Ten seconds are spent drawing electricity, but five seconds after switch A is turned on, switch B closes, enabling current to pass through the second resistor that is exactly the same.
• 

  Figure 2 Current–time graph.

• [math]\Delta Q = I * \Delta t [/math]
• The area under the current-time graph from t = 0s to t = 5s represents the charge transferred during the first 5s. The current doubles during the second five seconds.
• The region beneath the graph from t = 5s to t = 10s represents the charge transferred during this period.
• The whole area under the graph represents the total charge ∆Q transmitted during the course of the 10s time.
• [math] \Delta Q = Q_{0-5} + Q_{5-10} \\ \Delta Q = 2.0 \, \text{C} + 4.0 \, \text{C} \\  \Delta Q = 6.0 \, \text{C} [/math]
• The total charge transferred is the area under a current–time graph.

2. Potential difference and electromotive force:

• Only the speed at which charged particles—typically electrons—move through a circuit is measured by electric current.
• It provides no information on the electrical energy used in circuits.
• Potential difference (pd), represented by the symbol V and expressed in volts (V), is the SI unit used to represent the electrical energy in circuits.
• A voltmeter is placed across and in parallel with an electrical component to detect the potential difference across it.
• Potential difference, also known as voltage, is the difference in electric potential energy between two points in a circuit.
• It’s the driving force behind electric current.
• This electrical energy is transferred into heat, light and other more useful forms of energy by the components.
• [math] \text{Potential difference } V \, (\text{V}) = \frac{\text{Electrical work done by the charge } W \, (\text{J})}{\text{Charge flow } Q \, (\text{C})} \\ V \, (\text{V}) = \frac{\text{W} \, (\text{J})}{\text{Q} \, (\text{C})} \\ 1 \, \text{V} = 1 \, \text{J} \, \text{C}^{-1} [/math]
• On the other hand, the energy changes associated with power supplies like batteries, generators, and main power supply units cannot be well described by potential difference.
• These apparatuses convert many types of energy, such chemical energy, into electrical energy.
• The electromotive force (emf), represented by the symbol ε, is a new quantity that we define to distinguish between these various energy exchanges.
• Using a voltmeter, the values of emf and pd are expressed in volts, or symbol V.
• Electromotive force, is the energy provided by a source that drives electric current through a circuit.
• [math] electromotive force,\, \varepsilon \, (\text{V}) = \frac{electrical\, work\, done \,on\, the\, charge,\, E \, (\text{J})}{ charge flow,\, Q \, (\text{C})} \\ \varepsilon \, (\text{V}) = \frac{E \, (\text{J})}{Q \, (\text{C})} [/math]
• – Measured in volts (V)
  – The energy per unit charge that a source provides to drive current
  – Can be thought of as the “pressure” that pushes electric charge through a circuit
  – Can be generated by various sources, such as:
  • Batteries (chemical energy converted to electrical energy)
  • Generators (mechanical energy converted to electrical energy)
  • Solar cells (light energy converted to electrical energy)
• EMF is responsible for:
  – Driving electric current through a circuit
  – Overcoming resistance and energy losses in the circuit
  – Maintaining the flow of charge
• Some differences between EMF and potential difference (PD):
  – EMF is the energy provided by a source, while PD is the energy difference between two points.
  – EMF is the cause of current flow, while PD is the result of current flow.
• The law of conservation of energy can now be written in terms of emf and pd. In a series circuit, where the components are connected one after another in a complete loop.
• The total electrical energy per coulomb transferring into the circuit (the sum of the emfs in the circuit) must equal the energy per coulomb transferring into other forms of energy (the sum of the pds).
• 
  Figure 3 A circuit diagram with attach a battery provide potential difference
• Potential difference amount by volt meter.
• Electrical current measured by ampere mater.

3. Resistance:

• Resistance (R) is the opposition to the flow of electric current through a conductor. Here are some key points about resistance.

  
  Figure 4 Electric charges flow into
  a circuit with attach a resistance (R)

  – Measured in ohms (Ω).
  – Depends on the material, length, and cross-sectional area of the conductor.
  – Increases with increasing length and decreasing cross-sectional area.
  – Decreases with increasing temperature (in most cases).

• The substance of the circuit obstructs the passage of the charge when current passes through it, such as through the metal connecting wires.
• The oscillating positive ion cores of the metal structure are collided with by the electrons as they move through the metal on a tiny level.
• The electrons’ electrical energy is transferred to the metal’s structure via the collisions with the positive ion cores, which increases the vibration of the metal ion cores and heats the wire.
• As the temperature rises, so does the resistance.
• As the temperature rises, the positively charged, vibrating ion cores move around more and obstruct the passage of electrons.
• This is in opposition to the electron gas’s passage through the structure.
• Electrical insulators are parts that allow very little electricity to flow through them due to their high resistance.
• Certain materials exhibit little resistance at extremely low temperatures.
• We refer to these substances as superconductors.

⇒ Superconductors

• Superconductors are materials that exhibit zero electrical resistance when cooled to extremely low temperatures.
• This means that they can conduct electricity with perfect efficiency and without losing any energy.
• Here are some key points about superconductors:
  – Zero electrical resistance
  – Perfect conductivity
  – Can carry electrical current without losing energy
  – Exhibit the Meissner effect: expel magnetic fields
• Can be used in various applications, such as:
  -Magnetic Resonance Imaging (MRI) machines
  -High-energy particle accelerators
  -Magnetic levitation (maglev) trains
  -Power transmission lines
  -Quantum computing
•  Types of superconductors:
  – Low-temperature superconductors (LTS): require cooling to very low temperatures (typically below 30 K)
  -High-temperature superconductors (HTS): can exhibit superconductivity at relatively higher temperatures (typically above 30 K)

4. Current/potential difference characteristics and Ohm’s law:

• An electrical characteristic is a graph (usually I – V) that illustrates the electrical behavior of the component.
• Graphs illustrating the potential difference and current variations when a component is connected in both forward and reverse bias (i.e., when the current flows in one direction before changing to the other) are known as electrical characteristics.
• A fixed resistor’s electrical characteristic is the easiest to understand.
• 
  Figure 5 Electrical characteristic graphs of a fixed resistor
• To show the link between a current flowing through a component and the potential difference across a component, I–V graphs can be made using I or V on either axis.
• Given that the current flowing through a component is dependent upon the potential difference across it, I–V diagrams, where V is shown on the x-axis, are helpful.
• When constructing circuits for devices, this kind of graph comes in very handy for those who need to know how a component would react to various applied potential variations.
• A good tool for visualizing a component’s resistance is a V–I graph, which is typically used to depict the properties of batteries and cells.

⇒ Ohm’s law

• German scientist Georg Ohm experimented with potential difference and current on metal wires at constant temperature in 1827.
• Under the assumption that the temperature (and other physical factors) was constant, Ohm found that the current (I) flowing through the wire was proportionate to the potential difference (V) across the wire.
• An electrical characteristic graph will be linear if this is displayed on it.
• Ohm’s Law states that the current flowing through a conductor is directly proportional to the voltage applied across it, and inversely proportional to the resistance of the conductor.
• Mathematically, it’s expressed as:
• [math] I \propto V \\ V = I R [/math]
• When applied to metal wires at constant temperature, it is often a specific situation.
• However, by utilizing the idea of resistance, a practical, well-known mathematical equation may be created that defines the ohm (Ω), the unit of resistance, using the connection between I and V.
• [math] R = \frac {V}{I} [/math]
• Put differently, a component must have a resistance of 1Ω if a potential difference of 1V results in a current of 1A flowing through it.

  
  Figure 6 An electrical characteristic
  of a fixed resistor showing Ohm’s

• This formula is applicable in any situation and shows that a component with a large resistance, R, is implied to have a small measured current (I) for a fixed potential difference (V), and vice versa.
• Similar to this, in order to push a fixed current (I) through a big resistance(R) we need a large potential difference (V).
• The electrical properties of fixed resistors and metal wires at constant temperature are linear and they follow Ohm’s law throughout their current range.
• These kinds of parts are referred to as ohmic conductors since they adhere to Ohm’s law.
• The current flowing through an ohmic conductor is proportional to the potential difference applied across it.

⇒ Other electrical characteristics:

• As current passes through a conventional tungsten filament lamp, electrical energy is converted into both light and heat.

  
  Figure 7 Electrical characteristic
  of a filament lamp

• More kinetic energy is transferred when the current rises because there are more electron collisions with the tungsten lattice’s positive ion centers.
• The resistance rises as a result of the positive ion cores’ increased amplitude vibrations.
• A greater temperature is caused by a higher current, and a higher resistance follows from that.
• Figure 7 illustrates a filament lamp’s electrical characteristics.
• A non-ohmic component is a component that does not obey Ohm’s law; i.e. current is not proportional to the potential difference applied across it.
• No matter which way the current flows through them, components like filament bulbs and fixed resistors have the same properties.
• Both the forward and reverse bias forms on their V-I graphs are the same.
• This is not how components like semiconductor diodes behave.
• Typically used in electrical circuits, diodes function as one-way gates to stop current from returning to the source.
• Because they may be utilized in circuits to convert alternating current (ac) into direct current (dc), they are very helpful in major power supply.
• 
  Figure 8 A semiconductor diode – symbol and picture. The current will only flow in the direction of the arrow (anode to cathode).
• Diodes only conduct in forward bias, or in the direction indicated by the arrow on the symbol.

  
  Figure 9 Electrical characteristic
  of a semiconductor diode

• The component itself typically has a distinct colored ring at the forward bias end to indicate this orientation.
• Since diodes don’t conduct under reverse bias, their resistance is infinite in this situation.
• In forward bias, diodes have extremely low resistance.
• Typically, diodes’ electrical properties are shown as current (y-axis)–potential difference (x-axis) diagrams.

5. Thermistors:

• Thermistors are temperature-sensing devices that exhibit a change in electrical resistance when their temperature changes.
• They’re made from specialized materials that are designed to detect temperature changes.
• 
  Figure 10 Thermistor circuit symbol, resistance – temperature graph and shape
• Types of Thermistors:
  – NTC (Negative Temperature Coefficient) Thermistors: Resistance decreases as temperature increases
  – PTC (Positive Temperature Coefficient) Thermistors: Resistance increases as temperature increases
• Characteristics:
  – High sensitivity and accuracy
  – Fast response time
  – Low power consumption
  – Small size and low cost
• Applications:
  – Temperature measurement and control
  – Thermal protection and monitoring
  – Automotive and industrial applications
  – Medical devices and equipment
  – Consumer electronics and appliances
• At a low temperature of 20°C, the resistance of the thermistor is high and so the current (and the V/R ratio) is low.
• [math] R= \frac{V}{I} \\
  R = \frac{6 \, \text{V}}{0.002 \, \text{A}} \\
  R = 3000 \, \Omega [/math]
• A higher temperature of 80°C, the resistance is lower and the V/R ratio is higher.
• [math] R= \frac{V}{I} \\
  R = \frac{11 \, \text{V}}{0.010 \, \text{A}} \\
  R = 1100 \, \Omega [/math]
• The current flowing through the thermistor is therefore high.

6. Resistivity:

• Resistivity is a fundamental property of materials that describes their ability to resist the flow of electric current.
• It’s defined as the ratio of the electric field strength to the current density, and it’s typically denoted by the symbol ρ (rho).
• Resistivity is measured in units of ohm-meters (Ω m), and it’s a characteristic property of each material.

  
  Figure 11 Resistance and resistivity

• Some materials have high resistivity, meaning they resist current flow, while others have low resistivity, meaning they conduct current easily.
• Here are some key points about resistivity:
  – Resistivity is a tensor quantity, meaning it can have different values in different directions in an anisotropic material.
  – Resistivity is temperature-dependent, typically increasing with temperature.
  – Resistivity is affected by impurities, defects, and other material properties.
• As the conductor’s length (l) rises, more positive ion cores obstruct the flow of electrons through the conductor, raising the resistance (R). Actually, the resistance (R) doubles if the length (l), doubles. Thus, it follows that
• [math] R \propto I \qquad (1) [/math]
• The resistance of the conductor decreases with increasing cross-sectional area, A.
• In this case, if the cross-sectional area, A, doubles.
• [math] R \propto \frac{1}{A} \qquad (2) [/math]
• Combining both of these proportionality statements together:
• [math] R \propto \frac{1}{A}  [/math]
• and replacing the proportionality sign and adding a constant of proportionality, ρ, we have:
• [math] R = \text{const} \frac{l}{A} \\ R = \frac{\rho * l}{A} [/math]
• Where ρ (‘rho’) is called the electrical resistivity of the material.
• Resistivity is the property that gives the intrinsic resistance of the material independent of its physical dimensions, such as length and cross-sectional area.
• Resistivity has the units of ohm meters, Ωm, and is defined by the rearranged form of the equation:
• [math] \rho = \frac{R A}{l} [/math]
• where R is the resistance (measured in ohms, Ω).
• A is the cross-sectional area (measured in meters squared, [math] m^2 [/math]).
• l is the length (measured in meters, m).
• Certain intrinsic characteristics of a substance determine its resistivity.
• It specifically has to do with how many free, conducting electrons can pass through the structure and how easily these electrons can move across it.
• This mobility is influenced by the temperature of the material, the distribution of impurities, and the configuration of the atoms in the conductor.
• Temperature also affects resistivity.
• As temperature rises, the resistivity of metals increases, while many semiconductors—including silicon and germanium—have a decreasing resistance.
• When a superconducting substance, such as a metal, is heated below its critical temperature, its resistivity increases with decreasing temperature, but it becomes zero below.