Lecture 2 Notes: Current and Voltage

  • Electric Charge

    • A basic property of elementary particles
    • Exists as “Positive” and “Negative” charges
    • Measured in coulombs (C)
    • Represented by Q or q
    • One coulomb is extremely large compared to the charge of a single electron
    • Electron carries charge −1.6 × 10^{−19} C
    • Electron charge magnitude: |e| ≈ 1.6 × 10^{−19} C

  • Electric Current

    • The time rate of flow of electric charge
    • Measured in amperes (A)
    • 1 A = 1 C/s
    • Represented by I or i
    • I stands for intensity
    • Formal expression: i(t) = dq(t)/dt
    • Current is measured by an ammeter

  • Direct Current (DC) vs Alternating Current (AC)

    • “DC” Current: constant rate of flow
    • “AC” Current: most usage of AC means sinusoidal signals
    • Time-varying is more general and can include a zero-mean portion (AC) with a DC-offset
    • DC-offset concept: a constant component superimposed on an AC waveform
    • For DC, capitalized variables are used and the differential can be replaced by observations over a time interval Δt
    • DC relation: I = ΔQ/Δt = K, where K is a constant
    • For AC, a common form is: i(t) = A cos(ωt)

  • Current’s sign convention

    • The direction of current is defined as the direction of equivalent positive charge flow
    • If electrons move from left to right, the conventional current is from right to left
    • This convention follows the idea of positive-charge flow, not the actual motion of electrons
    • A reference resource is provided for illustration: explainxkcd discussion on current direction

  • Charge and Current: quick calculations

    • Q: What is the charge of 1 billion electrons?
    • Q = N × e = (10^9) × (−1.6 × 10^{−19}) C = −1.6 × 10^{−10} C
    • In a typical electronics circuit, 1 billion electrons may pass a cross-section of a wire every nanosecond
    • Q: What is the current in amps?
    • Relationship: I = ΔQ/Δt; 1 A = 1 C/s
    • Given: ΔQ = −1.6 × 10^{−10} C over Δt = 1 × 10^{−9} s
    • I = (−1.6 × 10^{−10} C) / (1 × 10^{−9} s) = −0.16 A
    • Magnitude answer: 0.160 A (direction depends on sign convention; the magnitude is 0.16 A)
    • Corresponding charge values for the electrons are negative; for current magnitude typically reported as +0.16 A

  • Voltage: the water analogy

    • If electrical charge is water and current is water flow, voltage is like the pressure difference that drives the flow
    • A path must be available for current to flow
    • This analogy helps intuition for why potential difference matters in circuits
    • Image source relates to a common teaching visualization

  • Voltage: comparison between two locations

    • Infinitely large sheets of charge create a uniform electric field (voltage field), represented by arrows
    • Voltage across two points in space is the energy required to move each unit of charge between those two points
    • Equivalently, the energy released when one unit of charge moves from a higher potential to a lower potential
    • Voltage is measured with a voltmeter in units of volts [V]
    • Formal definition: ΔV=ΔEΔQ\Delta V = \frac{\Delta E}{\Delta Q}
    • When a unit of charge is moved along the arrow-path between two points, energy (\Delta E) is transferred/shaped
    • Alternatively, one can view voltage as the energy per unit charge required or released when moving between two locations

  • Circuit schematic and the lumped circuit model

    • Circuit schematic: schematic diagram versus physical diagram (Figure 1: (a) schematic, (b) physical)
    • Lumped circuit model: an abstraction where circuit elements are considered lumped (concentrated at points) rather than distributed in space
    • Lumped elements include resistors (R), sources, and other components placed at discrete points
    • Nodes are the connection points in the circuit where components meet
    • The model emphasizes that the electrical behavior can be described without detailing spatial distribution within each element

  • Series circuits: definition and properties

    • Two or more elements connected along a single conductive path
    • If the current path through any one element is opened, no current passes through the other series elements
    • In a series configuration: the same current flows through all elements
    • Voltage across series elements adds: V_total = V1 + V2 + …
    • Example diagram typically shows elements such as R2, R3, RA, R5 with the same current I flowing through each

  • Parallel circuits: definition and properties

    • Two branches in parallel are connected such that the current can split between branches and then recombine
    • If the current path through one branch is broken, current can still flow through the remaining parallel branches
    • In a parallel configuration: voltages across all branches are the same (V_total is shared)
    • Currents in branches sum to the total current entering the node: I_total = I1 + I2 + …
    • The diagrams illustrate how R2, R3, R4, etc., are arranged in parallel paths

  • Series vs parallel: quick quiz format (as shown in the slides)

    • Q: Determine whether a given arrangement is Series, Parallel, Neither, or Both
    • Options: A. Series B. Parallel C. Neither D. Both
    • Purpose: reinforce criteria for identifying series vs parallel connections in circuits

  • Decorative lights: practical circuit connections

    • Question 1: Draw a circuit for 12 lightbulbs connected in series in one loop
    • Question 2: Draw a circuit for 12 lightbulbs connected in two parallel strands
    • This example highlights how series and parallel wiring affect current, voltage, and overall resistance in a circuit

  • L2 Learning Objectives

    • a) Compute relationships between charge, time, and current:
    • I=ΔQΔtI = \frac{\Delta Q}{\Delta t}
    • b) Define current and voltage:
    • Current: I=ΔQΔtI = \frac{\Delta Q}{\Delta t}
    • Voltage: V=ΔEΔQV = \frac{\Delta E}{\Delta Q}
    • c) Identify series and parallel elements in a circuit
    • Key constants and relationships mentioned:
    • 1 A=1 C/s1\,\text{A} = 1\,\text{C}/\text{s}
    • i(t)=dq(t)dti(t) = \frac{dq(t)}{dt}
    • For DC: I=ΔQΔt=K(constant)I = \frac{\Delta Q}{\Delta t} = K\quad(\text{constant})
    • For AC: i(t)=Acos⁡(ωt)i(t) = A \cos(\omega t)

  • Quick reference values and formulas

    • Electron charge: (e = 1.6 \times 10^{-19}\,\text{C}) (negative for electron)
    • Current definition: (I = \frac{\Delta Q}{\Delta t})
    • Unit conversion: (1\ \text{A} = 1\ \text{C}/\text{s})
    • Relationship between energy and charge: (\Delta V = \frac{\Delta E}{\Delta Q}) where (\Delta V) is in volts and (\Delta E, \Delta Q) are energy and charge changes respectively

  • Practical implications and connections

    • Understanding current direction helps in predicting how devices respond to different wiring configurations
    • Distinguishing DC vs AC is essential for designing power supplies and signal processing circuits
    • The lumped model simplifies complex circuits, enabling analysis using basic series/parallel rules
    • The decorative lights exercise demonstrates how topology affects current distribution and brightness

  • Notable symbols and terminology to remember

    • Charge: (Q) or (q)
    • Current: (I) or (i)
    • Voltage: (V) and energy per charge: (\Delta E/\Delta Q = \Delta V)
    • DC vs AC terminology and waveform shapes (sinusoidal for AC typical case)

  • References to visual aids and prompts in the lecture slides

    • The water-analogy figure helps intuition for voltage and current flow
    • Circuit schematics and lumped element models are introduced to bridge abstract concepts with physical circuits
    • Series/Parallel definitions are reinforced with diagrams and quick quiz questions