Slide 1

Drift velocity and resistance - Ohm’s Law (Conductivity and Resistivity)

• Conductivity and resistivity are two important properties of a material that determine its electrical behavior.
• The drift velocity of charge carriers is directly proportional to the applied electric field.
• Ohm’s Law states that the current flowing through a conductor is directly proportional to the voltage across it, at a constant temperature.
• The resistance of a material is the ratio of the voltage across it to the current flowing through it.
• The resistance of a conductor depends on its dimensions and material properties.
• Resistivity is a measure of how strongly a material opposes the flow of current.
• Conductivity is the reciprocal of resistivity and measures how easily a material conducts electric current.
• Ohm’s Law can be expressed as: V = IR, where V is the voltage, I is the current, and R is the resistance. Slide 2

Drift Velocity

• When an electric field is applied to a conductor, the free charge carriers (electrons or ions) experience a force that causes them to move.
• The average velocity of these charge carriers is called the drift velocity.
• It is important to note that the actual motion of individual electrons is random due to collisions with other particles. Slide 3

Relationship between Drift Velocity and Applied Electric Field

• The drift velocity of charge carriers is directly proportional to the applied electric field.
• Mathematically, we can express this relationship as: v = μE
  • v represents the drift velocity,
  • μ is the mobility of charge carriers, and
  • E is the electric field strength. Slide 4

Ohm’s Law

• Ohm’s Law relates the current flowing through a conductor to the voltage across it.
• It can be stated as: V = IR
• Here, V denotes the voltage, I represents the current, and R is the resistance. Slide 5

Resistance and Resistivity

• Resistance is a measure of how much a material opposes the flow of electric current.
• It is influenced by the dimensions and material properties of the conductor.
• The resistance of a conductor can be calculated using the formula: R = ρl/A
  • R denotes resistance,
  • ρ is the resistivity of the material,
  • l represents the length of the conductor, and
  • A is the cross-sectional area of the conductor. Slide 6

Conductivity

• Conductivity is a measure of how easily a material conducts electric current.
• It is denoted by the symbol σ and is the reciprocal of resistivity.
• Mathematically, conductivity can be expressed as: σ = 1/ρ Slide 7

Relation between Resistivity and Conductivity

• Resistivity (ρ) and conductivity (σ) are inversely proportional to each other.
• If a material has a high resistivity, it will have low conductivity, and vice versa. Slide 8

Conductors, Insulators, and Semiconductors

• Conductors are materials that offer low resistance to the flow of electric current, such as metals.
• Insulators are materials that offer high resistance and prevent the flow of electric current, like rubber or glass.
• Semiconductors are materials whose conductivity lies between that of conductors and insulators.
• The conductivity of semiconductors can be altered by various factors such as doping or temperature changes. Slide 9

Example: Calculating Resistance

• Let’s consider a copper wire with a length of 2 meters and a radius of 0.5 mm.
• The resistivity of copper is 1.68 x 10^-8 Ω.m.
• We can calculate the resistance of the wire using the formula: R = ρl/A

  • Given: l = 2 m, A = πr^2, r = 0.5 x 10^-3 m, ρ = 1.68 x 10^-8 Ω.m

  • R = (1.68 x 10^-8 Ω.m) x (2 m) / (π x (0.5 x 10^-3 m)^2) Slide 10

Example: Calculating Resistance (continued)

• Evaluating the expression, we find:

  • R = (1.68 x 10^-8 Ω.m) x (2 m) / (π x (0.5 x 10^-3 m)^2)

  • R = 0.034 Ω (approximately)

• Thus, the resistance of the copper wire is approximately 0.034 Ω. Slide 11

Factors Affecting Resistance

• The resistance of a material depends on several factors:
  • Length of the conductor: Resistance increases with an increase in the length of the conductor.
  • Cross-sectional area of the conductor: Resistance decreases with an increase in the cross-sectional area.
  • Temperature: In most cases, resistance increases with an increase in temperature.
  • Material properties: Each material has its unique resistivity that determines its resistance. Slide 12

Factors Affecting Conductivity

• The conductivity of a material is influenced by:
  • Presence of impurities: Impurities can either increase or decrease the conductivity of a material, depending on the type and concentration of impurities.
  • Temperature: Generally, the conductivity of metals decreases with an increase in temperature due to increased scattering of free charge carriers. Slide 13

Ohm’s Law in Various Circuits

• Ohm’s Law applies to various types of circuits:
  • Simple circuits with a single resistor: V = IR, where V is the voltage, I is the current, and R is the resistance.
  • Series circuits: The total resistance of series resistors is the sum of individual resistances, and the current is the same through each resistor.
  • Parallel circuits: The total current in a parallel circuit is the sum of the currents through each branch, and the voltage across each resistor is the same. Slide 14

Electrical Power and Energy

• Electrical power is the rate at which electrical energy is consumed or produced.
• It can be calculated using the formula: P = IV, where P is power, I is current, and V is voltage.
• The unit of power is the watt (W).
• Electrical energy is the product of power and time, given by the equation: E = Pt, where E is energy, P is power, and t is time.
• The unit of energy is the kilowatt-hour (kWh). Slide 15

Electric Current and the Human Body

• Electric currents can pose risks to human health:
  • High currents passing through the body can cause internal burns, muscle contractions, respiratory difficulties, and cardiac arrest.
  • The severity of the shock depends on the current, the duration of contact, the path of the current, and the resistance of the body.
  • Electrical safety measures should be followed to prevent accidents and injuries. Slide 16

Superconductivity

• Superconductors are materials with zero electrical resistance at low temperatures.
• Below a critical temperature, superconductors exhibit the Meissner effect and expel magnetic fields.
• Superconductors have various applications, including in magnetic resonance imaging (MRI), particle accelerators, and power transmission. Slide 17

Thermistors and Temperature Measurement

• Thermistors are temperature-sensitive resistors that exhibit a large change in resistance with temperature.
• They can be used for temperature measurement and control in various applications.
• The resistance of a thermistor decreases with an increase in temperature (negative temperature coefficient) or increases with an increase in temperature (positive temperature coefficient). Slide 18

Potential Difference and Electromotive Force (EMF)

• Potential difference (V) is the electric potential energy difference per unit charge between two points in a circuit.
• Electromotive force (EMF) is the electric potential energy per unit charge supplied by a source of electrical energy, such as a battery.
• EMF is responsible for driving the electric current in a circuit.
• It is important to note that EMF is not a force but rather a potential difference. Slide 19

Kirchhoff’s Laws

• Kirchhoff’s laws are fundamental principles in circuit analysis:
  • Kirchhoff’s first law, also known as the conservation of charge, states that the sum of currents entering a junction is equal to the sum of currents leaving the junction.
  • Kirchhoff’s second law, also known as the voltage law, states that the algebraic sum of the electric potential differences in any closed loop of a circuit is zero. Slide 20

Applications of Ohm’s Law and Resistance

• Ohm’s Law and the concept of resistance have numerous applications:
  • Designing electrical circuits and calculating the appropriate resistors.
  • Analyzing and troubleshooting electrical circuits.
  • Determining the power consumed by electrical devices.
  • Understanding the behavior of conductors and insulators.
  • Developing technologies such as semiconductors and superconductors. Slide 21

Applications of Ohm’s Law and Resistance (continued)

• Heat dissipation in electrical devices: The resistance of a conductor determines the amount of heat generated when current passes through it.
• Building electrical circuits for various applications such as lighting, communication systems, and power distribution.
• Developing electronic devices like computers, smartphones, and televisions.
• Understanding the behavior of electric charge and current in various materials and environments.
• Investigating the electrical properties of biological systems and medical applications. Slide 22

Example: Calculating Power

• Let’s consider a light bulb with a resistance of 50 Ω and a current of 2 A flowing through it.
• We can calculate the power consumed by the light bulb using the formula: P = IV
  • Given: I = 2 A, V = IR = (2 A) x (50 Ω) Slide 23

Example: Calculating Power (continued)

• Evaluating the expression, we find:

  • P = IV = (2 A) x (50 Ω) = 100 W

• Thus, the light bulb consumes 100 watts of power. Slide 24

Electric Shock and Safety Measures

• Electric shocks can occur when a person comes into contact with an electric current.
• Safety measures to prevent electric shocks include:
  • Insulating equipment and electrical wiring.
  • Grounding electrical circuits.
  • Using circuit breakers and fuses to protect against overcurrent.
  • Following safety procedures while handling electrical equipment.
  • Avoiding contact with electrical sources when wet or in the presence of conductive materials. Slide 25

Factors Affecting the Electrical Resistance of Conductors

• Temperature coefficient of resistance: Some materials have a positive or negative temperature coefficient, meaning their resistance changes with temperature.
• Cross-sectional area and length: A thicker and shorter conductor has lower resistance compared to a thinner and longer conductor.
• Temperature: Most conductors exhibit an increase in resistance with an increase in temperature.
• Material properties: Different materials have different resistivities, which affect their resistance. Slide 26

Ohmic and Non-Ohmic Conductors

• Ohmic conductors follow Ohm’s Law and have a linear relationship between the current and voltage.
• Non-Ohmic conductors do not follow Ohm’s Law and may have a non-linear relationship between current and voltage.
• Examples of non-Ohmic conductors include diodes, transistors, and gas discharge tubes. Slide 27

Power in Circuits

• Power in a circuit can be calculated using different formulas based on the available variables:
  • P = IV (for direct current)
  • P = I^2R (for direct current)
  • P = I^2R = V^2/R (for alternating current)
• These formulas help us calculate the power consumed or produced by an electrical device or circuit. Slide 28

Series and Parallel Resistors

• In series circuits:
  • The total resistance is the sum of all individual resistances.
  • The current is the same through each resistor.
  • The voltage across each resistor depends on its resistance.
• In parallel circuits:
  • The total resistance is the reciprocal of the sum of the reciprocals of all individual resistances.
  • The voltage across each resistor is the same.
  • The total current is the sum of the currents through each resistor. Slide 29

Electrical Conductivity of Solutions

• Some solutions can conduct electricity due to dissolved ions.
• Electrolytes are substances that produce ions when dissolved in a solvent and can conduct electricity.
• Strong electrolytes dissociate completely into ions, while weak electrolytes only partially dissociate.
• Non-electrolytes do not produce ions and cannot conduct electricity.
• The conductivity of a solution depends on the concentration of ions and temperature. Slide 30

Summary

• Ohm’s Law relates current, voltage, and resistance in a conductor.
• Drift velocity is the average velocity of charge carriers.
• Resistance is determined by the dimensions and material properties of a conductor.
• Resistivity and conductivity are properties that characterize a material’s resistance.
• Factors affecting resistance include length, cross-sectional area, temperature, and material properties.
• Ohm’s Law has various applications in circuit analysis, power calculations, and electronics.
• Safety measures should be followed to prevent electric shocks.
• Power in circuits can be calculated using different formulas.
• Series and parallel circuits have distinct characteristics.
• Electrolytes conduct electricity due to dissolved ions in a solution.