Chapter 20: Electric Current, Resistance, and Ohm's Law

Electric Current, Resistance, and Ohm's Law

  • Battery Connection: A battery connects positive and negative terminals through a wire, allowing electron movement from the negative to the positive terminal.

  • Electric Current Definition:

    • SI Unit: Ampere (A)

    • Definition: Rate of flow of charge.

    • 1 Ampere = 1 Coulomb per second.

  • Calculating Current (Truck Battery Example):

    • Given: 720 C of charge in 4.00 s.

    • Formula:
      I = \frac{AQ}{\Delta t}
      Therefore, compute current from these values.

  • Calculating Current (Calculator Example):

    • Given: 1.00 C of charge, current = 0.300 mA.

    • Find time, use the formula:
      t = \frac{Q}{I}

  • Simple Electric Circuit Overview:

    • A closed path with conducting wires connects a load to battery terminals.

    • Conventional current direction follows positive charge flow direction.

  • Particle Movement in Current:

    • Current, I , is charge rate through area A .

    • Positive charges move with the electric field; negative charges (electrons) move opposite.

    • The average velocity of moving charges is the drift velocity. v_d .

  • Calculating Electrons per Second in a Circuit:

    • Example: For 0.300 mA current, determine electrons moved/second:
      n = \frac{I}{e} where e is the elementary charge.

  • Drift Velocity and Current Relationship:

    • Drift velocity v_d is influenced by free charge density n and cross-sectional area A .

    • Formula: I = nqAv_d .

  • Lightning Strike Current Calculation:

    • Lightning transfers 10^{20} electrons in 2 ms.

    • Total charge: AQ = n * e = 10^{20} * (-1.60 × 10^{-19} C) = -16.0 C .

    • Average current: I = \frac{-16.0 C}{2 × 10^{-3 s}} = -8 kA .

  • Ohm's Law Basics:

    • Indicates current I is directly proportional to voltage V applied:
      I = \frac{V}{R} (where R is resistance).

    • Unit of resistance: Ohm ()

  • Resistive Circuits:

    • Voltage drop across a resistor matches the battery's voltage output.

    • Basic components: battery, resistors, wires forming a closed loop.

  • Calculating Resistance Using Current-Voltage Graphs:

    • Plot various voltages against currents measured to find resistance.

  • Resistance Fundamentals:

    • Resistance of an object depends on its shape and material.

    • For a uniform cylinder:
      R = \rho \frac{L}{A} (where \rho is resistivity).

  • Factors Affected by Temperature:

    • Resistivity changes with temperature; typically \rho = \rho_0(1 + \alpha \Delta T) .

    • Example temperature coefficients for various materials can be referenced.

  • Electric Power Relations:

    • Power ( P ) in a circuit defined as:
      P = IV ,
      P = \frac{V^2}{R}, and
      P = I^2R.

  • Calculating Cost of Electricity:

    • Calculate total energy based on power consumption over time:
      E = Pt

    • Cost = Power in kW x Time in hours x Cost per kWh.

  • Glossary of Key Terms:

    • Direct Current (DC): Flows in one direction.

    • Alternating Current (AC): Fluctuates sinusoidally.

    • Resistance (R): A property impeding current with units of ohms (Ω).

    • Drift Velocity (v_d): Speed of charge carriers under electric field influence.

    • Electric Power (P): Rate of energy supply (in watts).