Electrical Quantities & Ohm's Law - Vocabulary Flashcards

Coulomb's Law

• The force between electrostatic charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
• Formal expression (Coulomb's law):
  F = k \, \frac{q1 \, q2}{r^2}
• In SI units, the constant k ≈ $8.9875 \times 10^9\ \mathrm{N\,m^2/C^2}$.

Coulombs and Charge

• 1 coulomb (C) is the amount of charge moved by a current of 1 ampere in 1 second.
• 1 C equals approximately $6.25 \times 10^{18}$ electrons:
  1\ \mathrm{C} = 6.25 \times 10^{18}\ \text{electrons}

Conventional Current vs Electron Flow

• Conventional current flow: by convention, current is considered to flow from the positive (higher potential) to the negative (lower potential).
• Electron flow: actual charge carriers (electrons) move from the negative terminal toward the positive.
• Visual cues: Battery and Diode demonstrations are used to compare the two concepts.

The Ampere

• The ampere (A) is the unit of electric current.
• Definition: 1\ \mathrm{A} = \frac{1\ \mathrm{C}}{1\ \mathrm{s}}
• Instrument: Ammeter measures current in amperes.

Analogies for Current

• Analogies help relate electrical flow to familiar concepts:
  • Battery as a source of potential.
  • Pump analogy: flow rate corresponds to current.
  • Flow meters measure flow rate in units such as GPM (gallons per minute); in electricity, Coulombs per second correspond to amperes.
  • Ammeter measures the rate of charge passage (C/s).

Electron Flow

• In conductors, electrons drift and move from atom to atom as charge carriers.
• This contrasts with the traditional view of a hole-and-electron movement in some materials.

Direct Current (DC) vs Alternating Current (AC)

• DC: unidirectional current (one-way flow).
• AC: bidirectional current (flow reverses direction periodically).

The Basic Circuit

• A complete circuit path is required for electricity to flow.
• Closed circuit: a circuit with a complete path.
• Elements of a basic circuit include a source (battery), conducting path, and a load (device).

The Basic Circuit – Open vs Closed

• Closed circuit: complete path allowing continuous current flow.
• Open circuit: path is broken; current flow ceases.

The Basic Circuit – Switches

• A simple switch can open or close a circuit, controlling current flow.

Short Circuit

• Short circuit: an unintended, unusually low-resistance path that bypasses the intended load.

120-V Appliance Circuit

• Key components: circuit breaker, ungrounded (hot) conductor, grounded (neutral) conductor, grounding (safety).
• Load: motor or other appliance.
• Grounding provides a safety path for fault currents.

Grounding in 120-V Circuits

• The grounding conductor provides a low-resistance path to ground.
• An incomplete path to ground can prevent fault current from returning safely.

Apparent Speed of Electricity

• The fundamental idea: electrical impulses propagate rapidly, producing the impression of instantaneous effect in many practical cases.
• Signal propagation in conductors is near the speed of light, though specific speeds depend on the medium.

Apparent Speed of Electricity – Thought Experiment

• If a wire were wrapped around the Earth 10 times and the switch is closed, the light would appear to come on almost instantly due to rapid signal propagation.

The Volt (E or V)

• The volt is the unit of electric potential difference (voltage) — electrical pressure.
• Common notation: V or E for voltage; a voltmeter measures this quantity.
• Conceptual examples: voltages can be stacked (e.g., 0.6, 1.2, 1.8, 2.4, …, 9 V) in illustrative diagrams.

The Ohm

• The ohm (Ω) is the unit of electrical resistance.
• An ohmmeter measures resistance.
• Resistance is opposition to current flow.

Hydraulic Work (Power) – Horsepower (Hp)

• In hydraulic systems, Power can be described as:
  • Flow rate times pressure (in hydraulic terms): P ∝ Q × ΔP.
• Common units in hydraulics include:
  • GPM (gallons per minute) for flow
  • PSI (pounds per square inch) or PSID (pressure differential) for pressure
• Horsepower relationship in US customary units:
  \mathrm{HP} = \frac{Q\ (\text{GPM}) \times \Delta P\ (\text{psi})}{1714}
• In SI, power can also be computed as
  P = \dot{V} \cdot \Delta P
  where appropriate, with proper unit conversion.

The Watt (W)

• The watt is the unit of electrical power.
• Heat production in a resistor (e.g., incandescent lamp) demonstrates the relation between current, voltage, and resistance.
• Power scales in kW (kilowatts) for larger values.

Electric Work (Power) – Watts

• In DC circuits: P = V \times I where V is voltage (volts) and I is current (amperes).
• Power can also be expressed as:
  P = E I = I^2 R = \frac{E^2}{R}
• These relations are the core of Ohm's law in practical form.

James Watt and Horsepower

• Horsepower (HP) definitions:
  • 1\ \mathrm{HP} = 550\ \mathrm{ft\,lb/s}
  • 1\ \mathrm{HP} = 33{,}000\ \mathrm{ft\,lb/min}
  • 1\ \mathrm{HP} = 746\ \mathrm{W}
• James Watt contributed to mechanical power concepts and the steam engine.

BTU and Calorie

• BTU (British Thermal Unit): the amount of heat required to raise the temperature of 1 pound of water by 1 °F.
• Calorie (thermochemical): the amount of heat required to raise the temperature of 1 gram of water by 1 °C.
• Note: a distinction exists between thermochemical calories (cal) and food calories (Cal or kcal).

Power Units Conversion

• Key equivalences (US customary and metric conversions):
  • 1\ \mathrm{HP} = 746\ \mathrm{W}
  • 1\ \mathrm{HP} = 550\ \mathrm{ft\,lb/s}
  • 1\ \mathrm{W} = 0.00134\ \mathrm{HP}
  • 1\ \mathrm{BTU!/hr} = 0.293\ \mathrm{W}
  • 1\ \mathrm{W!\cdot!s} = 1\ \mathrm{J}
  • 1\ \mathrm{BTU} = 1050 \sim 1055\ \mathrm{J}
  • 1\ \mathrm{BTU!/hr} = 0.293\ \mathrm{W}
  • 1\ \mathrm{Cal} = 4.184\ \mathrm{J}
  • 1\ \mathrm{Cal\ (food)} = 4184\ \mathrm{J}
  • 1\ \mathrm{ft!- nbsp;lb} = 1.356\ \mathrm{J}
  • 1\ \mathrm{J} = 0.239\ \mathrm{cal}
  • 1\ \mathrm{cal\/s} = 4.184\ \mathrm{W}
  • 1\ \mathrm{Wh} = 3600\ \mathrm{J}
• These conversions enable cross-domain comparisons (electric, thermal, mechanical).

Watts – Additional Context

• A watt is equivalently a joule per second:
  1\ \mathrm{W} = \frac{1\ \mathrm{J}}{\mathrm{s}}
• A watt also equals a newton-meter per second:
  1\ \mathrm{W} = 1\ \mathrm{N\,m/s}

Elevator Problem (Example 2-1)

• Problem: An elevator must lift a load of 4000 lb to a height of 50 ft in 20 s.
• Work done:
  W = F \times d = 4000\ \mathrm{lb} \times 50\ \mathrm{ft} = 200{,}000\ \mathrm{ft\,lb}
• Power (rate):
  P = \frac{W}{t} = \frac{200{,}000}{20\ \mathrm{s}} = 10{,}000\ \mathrm{ft\,lb/s}
• Convert to HP:
  \text{HP} = \frac{P}{550} = \frac{10{,}000}{550} \approx 18.18\ \mathrm{HP}
• This confirms the required mechanical power to operate the elevator.

Ohm's Law

• In a DC circuit, current is directly proportional to voltage and inversely proportional to resistance:
  E = I \times R
• Common notations:
  • E or V for voltage (electromotive force)
  • I for current (amperes)
  • R for resistance (ohms)
• Derived forms:
  • I = \frac{E}{R}
  • R = \frac{E}{I}
• In symbols:
  • E = I R \quad \Rightarrow\quad I = \frac{E}{R} \quad \Rightarrow\quad R = \frac{E}{I}

Ohm's Law – Usage and Charts

• Ohm's Law can be extended to include power:
  • P = E I
  • P = I^2 R
  • P = \frac{E^2}{R}
• These relationships appear on simplified charts and interactive exercises in the course materials.

Example Problems (2-3 to 2-5)

• Example 2-3: Iron at 120 V with 8 A current:
  • Known: V = 120 V, I = 8 A
  • Power: P = E I = 120 \times 8 = 960\ \mathrm{W}
• Example 2-4: Hair dryer rated at 1000 W, connected to 120 V:
  • Known: P = 1000 W, V = 120 V
  • Current: I = \frac{P}{V} = \frac{1000}{120} \approx 8.333\ \mathrm{A}
• Example 2-5: Hotplate, P = 1440 W, I = 12 A; find resistance:
  • Using R = \frac{P}{I^2}
  • R = \frac{1440}{12^2} = \frac{1440}{144} = 10\ \Omega
  • Note: A misprint in the source material listed 100 Ω; the correct value is 10 Ω.

Unit Variables and Symbols (Recap)

• E (voltage, E or V) – electromotive force or potential difference.
• I (current, amperes, A).
• R (resistance, ohms, Ω).
• P (power, watts, W or P in equations).
• Ohm’s Law relationships summarize these variables:
  E = I R,\quad I = \frac{E}{R},\quad R = \frac{E}{I},\quad P = E I,\quad P = I^2 R,\quad P = \frac{E^2}{R}

Metric Prefixes and Engineering Notation

• Metric prefixes (engineering notation uses powers of 1000, i.e., 10^3 increments):
  • Tera (T) = 10^{12}
  • Giga (G) = 10^{9}
  • Mega (M) = 10^{6}
  • Kilo (k) = 10^{3}
  • Base unit
  • Deci (d) = 10^{-1}
  • Centi (c) = 10^{-2}
  • Milli (m) = 10^{-3}
  • Micro (µ) = 10^{-6}
  • Nano (n) = 10^{-9}
  • Pico (p) = 10^{-12}
• The prefixes help express large and small quantities conveniently (e.g., 10 MΩ, 50 mA).

SI-Derived Units (Selected)

• Frequency: Hertz (Hz) = 1/s
• Force: Newton (N) = kg·m/s^2
• Pressure: Pascal (Pa) = N/m^2
• Energy/Work: Joule (J) = N·m
• Power: Watt (W) = J/s
• Electric charge: Coulomb (C) = A·s
• Electric potential: Volt (V) = W/A
• Capacitance: Farad (F) = C/V
• Resistance: Ohm (Ω) = V/A
• Conductance: Siemens (S) = A/V
• Magnetic flux: Weber (Wb) = V·s
• Magnetic flux density: Tesla (T) = Wb/m^2
• Inductance: Henry (H) = Wb/A
• Luminous flux: Lumen (lm) = cd·sr
• Illuminance: Lux (lx) = lm/m^2

Summary of Key Points

• A coulomb is a quantity of charge; 1 C = charge moved by 1 A in 1 s, and equals about 6.25 \times 10^{18} electrons.
• The ampere is defined by the flow of 1 C per second: 1\ \mathrm{A} = \frac{1\ \mathrm{C}}{1\ \mathrm{s}}.
• Ohm's Law in DC circuits: E = I R with alternate forms I = \frac{E}{R},\; R = \frac{E}{I}.
• Power relationships: P = E I = I^2 R = \frac{E^2}{R}; for a resistor, power is the product of voltage and current, or a function of current and resistance.
• The watt is the unit of power: 1\ \mathrm{W} = 1\ \mathrm{J/s}; large-scale power is given in kilowatts (kW) or megawatts (MW).
• The volt is the unit of potential difference (electric pressure); the ohm is the unit of resistance; the ampere is the unit of current.
• Practical energy conversions include HP, BTU, and Calorie relationships; HP links mechanical work to electrical power via conversion factors, and BTU/Cal serve thermal energy contexts.
• In circuits, a complete path is required for current to flow; short circuits bypass loads and present minimal resistance, which can be dangerous.
• Metric prefixes and SI-derived units provide a consistent framework for expressing electrical quantities across scales.