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Lecture 3 - Basic Electrical Units

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  • Lecture title: "Lecture 3 - Basic Electrical Units" 📚. The page shows branding and a few fun phrases (e.g., "JOIN THE RESISTANCE!" 🚧 and campus/organization hints). No substantive content beyond orientation and branding.

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  • Today’s lecture (ECE 1004, Chapter 1): key topics include Voltage ⚡️, current 🌊, resistance 🚧; Passive Sign Convention; Ohm’s Law; Power Law.

  • Reading ahead: Start reading Chapter 2. 📖

  • Administrative note: First Quiz is today. 📝 (There is no class on Monday.)

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  • Lab logistics: Pick up oscilloscope and parts kit today (Fri 8/29), 9:00
    –12:00 or 3:00
    –5:00. 🛠

  • Free kit; need to stop by Whittemore room 219 with Hokie Passport or ID. 🆔

  • Dr. Milburn and TAs will hand you a kit and record your name; contact tylermilburn@vt.edu if issues. ✉

  • Lab 0 will involve checking your kit this weekend. ✅

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  • GobblerFest event: design teams, meet students, on the Drillfield from 4
    –7 PM. Free admission.

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  • Basic electrical units: four main quantities in circuits: 🔌

    1) Voltage (Volts, V) ⚡️

    2) Current (Amperes, A) 🌊

    3) Resistance (ohms, Ω) 🚧

    4) Power (Watts, W) 🔥

  • These are the four main constituents in circuits, forming the basis for analysis.

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  • Voltage: ⚡️- Measured in Volts (V). Also known as potential difference.

    • 1 Volt = 1 Joule / 1 Coulomb. Symbolically: 1\text{ V} = \frac{1\text{ J}}{1\text{ C}}

    • Voltage is the electrical potential between two points in a circuit.

    • Physical analogy: potential energy difference between two heights. ⛰ Higher potential energy corresponds to higher voltage; difference in height drives the flow.

    • Intuition: voltage is the push that moves charge from one point to another. ➡

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  • Current: 🌊- Measured in Amperes (A). 1\text{ A} = 1\text{ Coulomb / second}

    • Current is the rate of flow of electrical charge in a circuit, typically from high voltage to low voltage. ➡

    • Analogy: water flowing downhill; current is the rate of water flow. 💧

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  • Resistance: 🚧- Measured in Ohms (Ω).

    • Resistance measures how much a circuit element impedes current flow. 🚫

    • Analogy: friction or a pipe neck that restricts water flow. 🚿

    • Key idea: low resistance allows more current; high resistance restricts current. impeded

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  • Important distinction: the physical size of the conducting path affects resistance. 📏- A thicker wire (or a larger pipe) offers less resistance and can carry more current than a thin wire.

    • The difference in the ability to carry current is what we call resistance.

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  • Power: 🔥- Measured in Watts (W).

    • Power is the rate of energy transfer from one potential to another. ➡

    • Power is proportional to both the voltage difference and the current: higher voltage and higher current mean more power transfer. ⬆

    • Analogy: the rate at which the potential energy is converted into kinetic energy as water flows downhill. 🏞

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  • Watts and kilowatt-hours (kWh): 💡- Power equation: P = V \times I where P is in Watts if V is in Volts and I in Amperes.

    • Energy relation: \text{Energy} = \text{Power} \times \text{Time}

    • Unit conversions:

    • 1\text{ Watt} = 1\text{ Joule per second}

    • 1\text{ kilowatt-hour (kWh)} = 1000\text{ Watts} \times 3600\text{ seconds} = 3.6 \times 10^6\text{ J}

    • 1\text{ kilowatt} = 1000\text{ Watts}

  • Note: In many practical contexts energy consumption is billed in kWh. 💲

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  • Cost of energy (example): Air conditioner operates at 240 V and 20 A. 💰- Power: P = V \times I = 240 \times 20 = 4800\ \text{W} = 4.8\ \text{kW}

    • Energy over half a day (12 hours): \text{Energy} = P \times t = 4.8\ \text{kW} \times 12\ \text{h} = 57.6\ \text{kWh}

    • Cost calculation (Virginia rate given as $0.124 per kWh in this slide):

      \text{Cost} = 57.6\ \text{kWh} \times 0.124\ \$ / \text{kWh} = \$6.91\ \text{per day}

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  • Electric Power dimensional analysis: 📊- Power can be written as P = V \times I.

    • In base units, 1\ \text{W} = 1\ \text{J} / \text{s}.

    • Conceptually: Power is energy transferred per unit time. ⏱

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  • (Reiteration) Recall: Watts and kilowatt-hours – Power = Voltage × Current; Units: Watts = Volts × Amps; Energy = Power × Time; Units: kilowatt-hours = watts × 3600 seconds; 1 kilowatt = 1000 watts. ✅

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  • Cost of energy (alternate rate): Another example using $0.11 per kWh: 💲- P = V \times I = 240 \times 20 = 4800\text{ W} = 4.8\text{ kW}

    • \text{Energy} = 4.8\ \text{kW} \times 12\text{ h} = 57.6\text{ kWh}

    • \text{Cost} = 57.6 \times 0.11 = \$6.34\text{ per day}

  • Takeaway: The energy cost depends on power, usage duration, and the rate per kWh. 💡

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  • Electrical current definition (conceptual): 🌊- Current is the time rate of flow of charge through a conductor or circuit element. ➡

    • Charge has units of Coulombs; electrons carry negative charge. ⚛

    • Current units are amperes (A), equivalent to Coulombs per second (C/s).

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  • Mathematical view of current: ➕- Current is the rate of change of charge: i(t) = \frac{dq}{dt}

    • Charge as a function of time: q(t) = \int i(t) \; dt + q(0)

    • In words: the amount of charge that passes a point per unit time is the current; the total charge accumulated is the time integral of current. ⏳

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  • Do electrons move at the speed of light? No. 💨- Electrons physically drift slowly through a conductor (roughly on the order of a fraction of a meter per day for individual electrons; effectively slow drift velocity). 🐢

    • The electromagnetic signal propagates through the conductor at a speed close to the speed of light, carrying energy via the electromagnetic field. 🚀

    • Analogy: field propagation is like a Newton’s Cradle transferring energy quickly, even though individual balls move only short distances. 🎱

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  • Rationale for electron-flow picture in this course: 💡- For ECE 1004, we simplify to a flow of electrons to reason about circuits without introducing full electromagnetics fields. Fields are introduced later (e.g., in 2214 Physical Electronics).

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  • Energy transfer and sign convention: 🔋- Energy is transferred when charge flows through an element with a voltage across it.

    • A resistor never supplies energy; it absorbs energy (dissipates as heat). 🔥

    • Uphill energy transfer occurs when a battery/source pushes energy into the circuit. ⬆

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  • Current variables in circuit analysis: 🔠- We typically assign current variables such as i1, i2, i3.

    • Current flow directions can be chosen arbitrarily (a common teaching technique that simplifies analysis; the math will handle sign). 📐

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  • Current reference directions: 🧭- Reference direction for i_ab points from node a to node b.

    • Reference direction for i_ba points from node b to node a.

    • Relationship: i{ab} = - i{ba}.

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  • Emphasis of passive vs active energy transfer: ➡⬅- Downhill: resistor (energy absorption) versus uphill: battery/source (energy delivery).

    • The phrase reinforces the idea that energy is absorbed by passive elements and delivered by active sources.

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  • Voltages and charge: voltage vab is energy transferred per unit charge from point a to b. ⚡️- Units: volts (V) = joules per coulomb (J/C).

    • Elementary charge: e = 1.602177 \times 10^{-19}\text{ C} \approx 1.6 \times 10^{-19}\text{ C}.

    • One Coulomb equals approximately 6.242 \times 10^{18}\text{ electrons}.

    • Charge conventions: charge of an electron is negative; charge of a proton is positive. ⚛

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  • Reference directions for voltages: 🧭- The voltage vab has a reference polarity positive at a and negative at b.

    • This implies v{ab} = -v{ba}.

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  • Another reference direction note: ↔- In some textbooks, voltages are referenced with the positive direction at the head of an arrow; this convention is common but often not used in practice.

    • The key is to be consistent with voltage polarity and current direction.

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  • When unknown: you can assign voltage variables and reference polarities arbitrarily if you later relate them to current directions. ❓- Boxes symbolize unspecified circuit elements; the important step is to relate voltage polarities to current directions as analysis proceeds. ➡

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  • Passive Sign Convention (PSC): ✅- If current flows from high potential to low potential (from + to −), then the current is considered positive.

    • If current flows from low potential to high potential (from − to +), the current is negative.

    • Recall: Power = Voltage × Current. 💡

    • Positive power means energy is absorbed by the element (passive element like a resistor); negative power means energy is delivered by the element (like a source). 🔋

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  • PSC specifics used in ECE: ➕➖- Positive current (positive power) when current direction aligns with the passive sign convention (flow from + to − across the element).

    • Negative current (negative power) when current direction is opposite to passive sign convention (element delivering power).

    • Remember: Power is positive for absorption, negative for delivery.

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  • Ohm’s Law and the relationship between R, V, and I: 📐- V = I \times R

    • If you have a resistance R with current I flowing, there is a voltage drop V across the resistance.

    • Infinity resistance (R \to \infty) implies current I \to 0 (I = V/R).

    • Zero resistance (R \to 0) with a voltage across it would imply current tends to infinity (I = V/R), which is idealized and non-physical in real circuits. ⚠

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  • Ohm’s Law forms and units: 📏- V = I \times R

    • R = V / I

    • I = V / R

    • The mnemonic circle diagram to memorize V, I, R relations: V at the top, with I and R forming the other links (V = IR, I = V/R, R = V/I). ⭕

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  • Resistors in practice: ⚙- Carbon film resistors are common components in kits. 🛠

    • Resistors are used to adjust voltages and currents to desired values.

    • They drop voltage when current flows through them, converting some electrical energy into heat energy. 🔥

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  • Resistor color codes: 🌈- Example: 47000\text{ Ω} = 47\text{ kΩ}.

    • The course mentions a chart (color code card) provided in the kit to read resistor values. 💳

    • Capacitors and inductors are similarly color-coded or labeled for value identification.

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  • Sign convention caveat: 🚫- If the voltage reference for an element is opposite to the passive configuration, the voltage is v = -Ri.

    • This yields a negative voltage (voltage drop opposite to assumed polarity).

    • Positive current flows from positive to negative voltage in the passive convention; if current is shown opposite to this direction, the current is negative.

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  • Three forms of Ohm’s Law and memorization aid: 💡- I = V / R

    • V = I \times R

    • R = V / I

    • A circle diagram is used to help memorize these, with V at the top of the circle. ⭕

  • This recaps Ohm’s Law and reaffirm the units involved. ✅

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  • Example applications of Ohm’s Law (illustrative problems): ➕- If V = 20 V and R = 4 Ω, then I = V/R = 5 A.

    • If R = 12 Ω and I = 3 A, then V = IR = 36 V.

    • If V = 6 V and I = 3 A, then R = V/I = 2 Ω.

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  • Additional derived results for Ohm’s Law (confirmations): ✅- For V = 20 V and R = 4 Ω, I = 5 A.

    • For I = 3 A and R = 12 Ω, V = 36 V.

    • For V = 6 V and I = 3 A, R = 2 Ω.

  • These reinforce the consistency of Ohm’s Law across the three forms.

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  • Power dissipation in a resistor (combining Ohm’s Law with Power Law): 🔥- From P = VI and V = IR, we can derive:

    • P = I \times V = I \times (I \times R) = I^2 R

    • P = V \times I = (V) \times I

    • P = V^2 / R

    • All four equivalent forms:

    • P = VI

    • P = I^2 R

    • P = V^2 / R

    • Note: We can substitute current or voltage interchangeably via Ohm’s Law to obtain the third form. 🔄

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  • Practice: find the power of each element using the relationships above. (The slide shows several layout-based problems; the key idea is to compute P with one of the three equivalent formulas, ensuring consistency with the given V, I, and R values. Common cases include P = VI, P = I^2 R, and P = V^2 / R.) ✍

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  • Worked power examples (illustrative): 💡- If a component has V = 20 V and R = 4 Ω with I = 1 A (as a scenario):

    • P = VI = 20 \times 1 = 20\text{ W}

    • If a component has V = 12 V and R = 12 Ω with I = 1 A (scenario):

    • P = I^2 R = 1^2 \times 12 = 12\text{ W}

    • If a component has V = 6 V and I = 3 A: R = V / I = 2 Ω and P = VI = 6 \times 3 = 18\text{ W}

  • Sign convention note: The slides show signs indicating whether power is absorbed (+) or delivered (−) by an element, consistent with the Passive Sign Convention. ➕➖

  • Example conclusions (using PSC): ✅- A resistor absorbing energy has positive P (e.g., +100 W). 🔥

    • A source delivering energy has negative P (e.g., −100 W). 🔋

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  • Summary of key points: ⭐- Passive Sign Convention (PSC) links voltage polarity with current direction. 🔗

    • Currents flowing from high potential to low potential are considered positive under PSC. ➡

    • Currents flowing from low potential to high potential are considered negative under PSC. ⬅

    • Positive power = energy absorbed by a component (passive element like a resistor). 🔥

    • Negative power = energy delivered by a component (source or battery). 🔋

    • Always remember the Passive Sign Convention when analyzing circuits. ✅

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  • Quiz information and a lighthearted aside: Canvas quiz access and a humorous aside about electric spark myths (electrodermal activity). 📝⚡️

  • Practical reminder: Be prepared to take the quiz via Canvas. 💻

  • Overall note on connections and relevance: 🌐

    • The material ties together core concepts used in circuit analysis: how voltage, current, and resistance relate (Ohm’s Law), how energy transfer is quantified (Power and kWh), and how to correctly assign sign conventions to understand whether elements are absorbing or delivering power.

    • Foundational ideas include modeling current as a flow of charge, acknowledging that real charge carriers move slowly but signals propagate quickly via electromagnetic fields, and using