Chapter 9: Current

Introduction to Current and Resistance

  • Chapter Overview: This chapter discusses various aspects of electrical current, resistance, and energy, including:
      - 9.1 Electrical Current
      - 9.2 Model of Conduction in Metals
      - 9.3 Resistivity and Resistance
      - 9.4 Ohm's Law
      - 9.5 Electrical Energy and Power
      - 9.6 Superconductors

9.1 Electrical Current

  • Electrical Current: Defined as the rate of flow of charge through a material.

  • Unit of Measurement: The standard unit for electrical current is the ampere (A), defined as one coulomb of charge passing through a cross-sectional area per second.

  • Drift Velocity: In conductors, the charges move not in straight lines but rather undergo collisions, leading to a drift velocity wherein electrons travel through a material while losing kinetic energy to the material. This behavior is akin to an object falling through a medium where it reaches terminal velocity.

  • Importance Related to Electric Shock: When considering electric shock, the current is the critical factor impacting damage rather than the voltage.

  • Current Formula: The average current can be mathematically described:
      - I=racQtI = rac{Q}{t}
      - where:
        - II = average electrical current
        - QQ = amount of net charge
        - tt = time for which charge flows

  • Examples:
      - Average Current Calculation: A truck battery moves 720 C of charge in 4 s. The average current during this operation can be calculated directly from the above formula.
      - Instantaneous Current Calculation: The instantaneous current can be calculated using the limit as time approaches zero:
        - I(t)=racdQdtI(t) = rac{dQ}{dt}

  • Analyzing Electric Current through a Wire: The schematic representation and the flow of conventional current are illustrated:
      - Current direction is often from the positive terminal of a battery to the negative; thus, in metal wires, the flowing particles are predominantly electrons, which move in the opposite direction of the conventional current.

9.2 Model of Conduction in Metals

  • Understanding Electron Movement:
      - Electrons in conducting wires do not have a uniform velocity but bounce randomly as they collide with atoms.
      - The drift velocity represents the average velocity in the direction of the electric field due to these collisions.

  • Charge Transport: The free electrons in metals can be modeled as an incompressible fluid; when electrical signals are applied to the medium, they propagate rapidly due to a rapid change in the electric field.

  • Drift Velocity Equation:
      - The relationship between current and drift velocity is established:
        - I=nimesAimesqimesvdI = n imes A imes q imes v_d
      - where:
        - nn = number density of free charge carriers
        - AA = cross-sectional area
        - qq = charge of each carrier
        - vdv_d = drift velocity

  • Comparison to Incandescent Bulbs: When electrical energy runs through an incandescent bulb, it transforms into light and heat energy, demonstrating direct conversion and the operational principle of electric circuits.

9.3 Resistivity and Resistance

  • Resistivity Definition: The intrinsic property of materials that quantifies how strongly a material opposes the flow of electrical current, typically denoted by <br>ho<br>ho.

  • Resistance Definition: A practical characteristic of a specific conductor described by:
      - R=<br>horacLAR = <br>ho rac{L}{A}
      - where:
        - RR = resistance of the conductor
        - LL = length of the conductor
        - AA = cross-sectional area

  • Temperature Coefficient and Resistance Changes:
      - As the material temperature increases, its resistivity commonly increases in metals:
        - <br>ho(T)=<br>ho0[1+β(T−T0)]<br>ho(T) = <br>ho_0[1 + \beta(T - T_0)]
      - where β\beta represents the temperature coefficient of resistivity.

  • Conductivity and Its Relation to Resistivity: The reciprocal of resistivity gives the conductivity of a material, a significant metric for engineering applications in circuits.

9.4 Ohm's Law

  • Description: Ohm's Law expresses the relationship between current (I), voltage (V), and resistance (R) as:
      - V=IRV = I R

  • Empirical Law: This law applies linearly in ideal scenarios, showing that the current through a conductor is proportional to the voltage across it, assuming the temperature remains constant.

  • Verification through Experimentation: Ohm constructed devices to reliably measure voltage and current relationships, confirming the practical application of his law across resistive elements in circuits.

9.5 Electrical Energy and Power

  • Power Description: Power in an electric circuit is calculated through multiple formulations, with a critical equation:
      - P=IV=I2R=racV2RP = I V = I^2 R = rac{V^2}{R}

  • Dissipation of Energy: Electrical energy converts into different forms, such as heat in resistive components, illustrating the transformations occurring in practical electrical applications.

  • Cost of Electricity: Discusses the importance of energy efficiency and cost-effectiveness when considering different appliances and their power ratings.