Electrical quantities and units form the backbone of circuit analysis. They help us understand how electricity flows and interacts in systems. From current and voltage to resistance and power, these concepts are essential for grasping the fundamentals of electrical circuits.

Mastering these units and their relationships is crucial for solving circuit problems. Whether you're dealing with tiny microamps or massive megawatts, knowing how to convert between units and apply Ohm's Law will make your journey through electrical engineering much smoother.

Electrical Quantities

Fundamental Electrical Quantities

• Current (I) represents flow of electric charge through a conductor, measured in amperes (A)
• Voltage (V) denotes electric potential difference between two points in an electrical circuit, measured in volts (V)
• Resistance (R) signifies opposition to electric current flow in a conductor, measured in ohms (Ω)
• Free electron movement in a conductor causes current, while voltage drives this movement
• Material properties and factors (temperature, length, cross-sectional area) affect resistance
• Conductance (G) represents ease of current flow through a material, measured in siemens (S)
  • Reciprocal of resistance: $G = \frac{1}{R}$

Derived Electrical Quantities

• Electrical power (P) measures rate of energy transfer in a circuit, measured in watts (W)
  • Calculated using current and voltage: $P = VI$
  • Alternatively expressed using resistance: $P = I^2R$ or $P = \frac{V^2}{R}$
• Electrical charge (Q) quantifies amount of electricity, measured in coulombs (C)
  • One coulomb equals charge transferred by one ampere current in one second
• Electrical energy (E) represents work done by electrical forces, measured in joules (J) or kilowatt-hours (kWh)
  • Calculated as product of power and time: $E = P \times t$

Current, Voltage, and Resistance

Ohm's Law and Circuit Relationships

• Ohm's Law establishes fundamental relationship between current, voltage, and resistance
  • Mathematically expressed as: $V = IR$
• Series circuits maintain constant current while voltages add up
  • Total resistance in series: $R_{total} = R_1 + R_2 + R_3 + ...$
• Parallel circuits keep voltage constant while currents add up
  • Total resistance in parallel: $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$
• Kirchhoff's Current Law (KCL) states sum of currents entering a node equals sum of currents leaving it
  • Mathematically: $\sum I_{in} = \sum I_{out}$
• Kirchhoff's Voltage Law (KVL) asserts sum of all voltages around any closed loop in a circuit equals zero
  • Mathematically: $\sum V = 0$

Factors Affecting Electrical Quantities

• Temperature influences resistance of materials
  • Most metals increase resistance with temperature (positive temperature coefficient)
  • Some semiconductors decrease resistance with temperature (negative temperature coefficient)
• Length of conductor directly proportional to resistance
  • Longer conductors have higher resistance
• Cross-sectional area of conductor inversely proportional to resistance
  • Thicker conductors have lower resistance
• Material composition affects conductivity and resistance
  • Copper and silver have low resistance (good conductors)
  • Rubber and glass have high resistance (good insulators)

Units for Electrical Quantities

Base Units and Their Multiples

• Ampere (A) measures current
  • Subdivisions include milliampere (mA) and microampere (μA)
  • 1 mA = 0.001 A, 1 μA = 0.000001 A
• Volt (V) quantifies voltage
  • Common variations include millivolt (mV) and kilovolt (kV)
  • 1 mV = 0.001 V, 1 kV = 1000 V
• Ohm (Ω) represents resistance
  • Multiples include kilohm (kΩ) and megohm (MΩ)
  • 1 kΩ = 1000 Ω, 1 MΩ = 1000000 Ω
• Watt (W) measures electrical power
  • Derived from product of volts and amperes
  • 1 W = 1 V × 1 A

Derived Units and Relationships

• Coulomb (C) quantifies electrical charge
  • Relationship to current: 1 C = 1 A × 1 s
• Joule (J) measures electrical energy
  • Relationship to power: 1 J = 1 W × 1 s
• Kilowatt-hour (kWh) commonly used for practical energy measurements
  • 1 kWh = 1000 W × 3600 s = 3,600,000 J
• Farad (F) measures capacitance
  • Relationship to charge and voltage: $C = \frac{Q}{V}$
• Henry (H) quantifies inductance
  • Relationship to voltage and current change: $L = \frac{V}{\frac{dI}{dt}}$

Unit Conversions for Electrical Quantities

Metric Prefix System

• Metric prefixes denote multiples and submultiples of electrical units
  • Milli- (m) represents 10^-3 (0.001)
  • Micro- (μ) signifies 10^-6 (0.000001)
  • Kilo- (k) indicates 10^3 (1000)
  • Mega- (M) denotes 10^6 (1000000)
• Conversion between units involves multiplying or dividing by powers of 10
  • 5.6 kV to V: 5.6 × 1000 = 5600 V
  • 2.3 mA to A: 2.3 ÷ 1000 = 0.0023 A

Engineering Notation and Practical Conversions

• Engineering notation expresses very large or small quantities using powers of 10 in multiples of 3
  • 4700000 Ω written as 4.7 × 10^6 Ω or 4.7 MΩ
  • 0.0000033 F expressed as 3.3 × 10^-6 F or 3.3 μF
• Prefixes combine with base units to create scaled units
  • mV (millivolt), kΩ (kilohm), MA (megampere)
• Converting between related quantities requires consideration of reciprocal relationships
  • 2 kΩ to mS: $\frac{1}{2000} = 0.0005 S = 0.5 mS$
• Practical applications involve recognizing and converting units in datasheets and specifications
  • 500 mV to V for voltage sensor range: 500 ÷ 1000 = 0.5 V
  • 25 μA to mA for LED current rating: 25 ÷ 1000 = 0.025 mA