11725_lecture5_2025_electricity II_(Canvas)

Lecture Overview

  • Lecture conducted by J. Woolnough.

  • Based on Pasquale et al. (2024), chapters 23 and 24.

  • Context: Electricity II, 2025 Semester 1.

  • Lecture available via Adrian Dusting at Canberra University.

Learning Objectives

  • Describe the motion of electric charges in relation to the electric field.

  • Explain concepts of electrical current, resistance, and power.

  • Distinguish between series and parallel circuits.

  • Understand and apply Ohm’s Law.

Fundamental Concepts

Electric Charges

  • Like charges repel each other, while opposite charges attract.

  • The electrical force increases with the magnitude of charge and decreases with distance.

  • Coulomb's Law Formula:

  • ( F = k \frac{Q_1 Q_2}{r^2} ) where

    • ( Q ) = charge,

    • ( r ) = distance,

    • ( k ) = constant.

Electric Potential

  • Electric potential increases with distance and the amount of charge.

  • Doing work (energy transfer) leads to an increase in potential.

  • Voltage: Measured as potential energy per charge.

    • Formula: ( ext{Voltage} (V) = 1 ext{ J/C} )

Electric Current

  • Electric current refers to the movement of charge.

  • It is measured as a rate (charges per unit time).

  • Coulomb: 1 Coulomb/second = 1 Ampere (1 A).

  • Formula: ( I = \frac{q}{t} )

Electrical Power

  • Power is the rate at which work is done and depends on work done per unit time.

  • Formula: ( P = \frac{W}{t} )

    • Units: Joules/second = Watts (W).

  • Other relationships include:

    • ( P = IV )

Voltage and Current

  • Distinction between voltage and current:

    • High voltage, low current can be safe (e.g., Van der Graaff generator).

    • Modest voltage and current can be hazardous (e.g., household circuits).

Electric Field Strength

  • Formula for Electric Field (E):

    • ( E = \frac{F}{q} )

    • Units: Newtons/Coulomb.

    • Direct relation: ( E = \frac{V}{d} ) (where (d) is distance).

    • Units: 1 N/C = 1 V/m.

Resistance and Ohm's Law

  • Resistance (R) measures impediment to current flow.

    • Units: Ohms (Ω).

  • Ohm’s Law states:

    • Current (I) directly proportional to electric potential (V) and inversely proportional to resistance (R).

    • Formulas:

      • ( I = \frac{V}{R} )

      • ( I \propto V )

      • ( V \propto \frac{1}{R} )

Conductivity

  • Conductivity is the inverse of resistance, indicating how easily current can flow for a given voltage.

  • Units of conductivity: Siemens (S).

    • 1 S = 1 Ω^{-1}.

Series and Parallel Circuits

Series Circuits

  • Current remains the same throughout.

  • Voltage divides across each resistor in series.

  • Formula:

    • ( V_T = V_1 + V_2 + ... + V_n )

Parallel Circuits

  • Current is divided among the branches.

  • Voltage across each branch remains constant.

  • Formulas:

    • ( I_T = I_1 + I_2 + ... + I_n )

    • Voltage: ( V_T = V_1 = V_2 )

Ohm's Law Examples

  • Problems allocating current and voltage across light globes in a circuit with values provided in Ohm's law format (e.g., ( V = IR )).

Summary

  • Concepts summarized include:

    • Electric potential (voltage)

    • Power

    • Current and Ohm’s Law

    • Electric field

    • Series circuit (voltage divider)

    • Parallel circuit (current divider)

  • Coulomb’s Law: ( F = k \frac{Q_1 Q_2}{r^2} )

  • Ohm’s Law summary: ( I = \frac{q}{t} ), ( V = IR ), ( P = \frac{W}{t} ), ( P = IV )

Course Progression

  • Recap of previous lectures on forces, work/energy, fluids, and electrostatics leading up to the current lecture.

  • Upcoming topics include heat, thermodynamics, waves, light, atomic physics, and nuclear physics.

Remembering Key Concepts

  • “With great power comes great current squared times resistance.”

  • A quote that connects to Ohm’s Law.