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).