Voltage, current, and power form the foundation of electrical circuits. These concepts help us understand how energy flows and transforms in electrical systems, from simple battery-powered devices to complex power grids.

Mastering these basics is crucial for analyzing circuits and designing electrical systems. By grasping voltage, current, and power relationships, you'll be able to tackle more advanced topics and solve real-world electrical engineering problems with confidence.

Voltage, Current, and Power

Fundamental Electrical Concepts

• Voltage represents electric potential difference between two points in a circuit, measured in volts (V)
  • Quantifies energy per unit charge available to move electrons through a conductor
  • Provided by voltage sources (batteries, power supplies)
• Current measures flow rate of electric charge through a circuit, measured in amperes (A)
  • Quantifies number of electrons passing through a point in a circuit per unit time
  • Conventional current flows from positive to negative, electron flow opposite direction
• Power calculates rate of energy transfer or conversion in electrical systems, measured in watts (W)
  • Represents amount of work done per unit time
  • Fundamental equation: $P = VI$, where P is power, V is voltage, I is current

Circuit Analysis Principles

• Polarity of voltage and direction of current flow crucial for accurate circuit analysis
• Ground or reference point essential for measuring and analyzing voltages
• Energy conservation applies to electrical power calculations
  • Total power supplied equals total power consumed in a circuit
• Efficiency in power transfer and conversion often expressed as percentage of output to input power
• Kirchhoff's Laws govern current and voltage behavior in circuits
  • Current Law (KCL): Sum of currents entering a node equals sum of currents leaving
  • Voltage Law (KVL): Sum of voltages around any closed loop equals zero

Calculating Electrical Power

Power Equations and Applications

• Fundamental power equation: $P = VI$
• Variations based on Ohm's Law:
  • $P = I²R$
  • $P = V²/R$
  • R represents resistance in ohms
• DC circuits always have positive power
• AC circuits can have:
  • Positive power (real power)
  • Negative power (reactive power)
  • Combination (apparent power)
• Power ratings crucial for proper circuit design and safety considerations
  • Determine maximum safe operating conditions for components (resistors, transistors)
  • Guide selection of appropriate power supplies and cooling systems

Power in Complex Circuits

• Superposition principle allows analysis of circuits with multiple sources
  • Consider each source independently
  • Sum their effects for total circuit behavior
• Power transfer and efficiency important in electrical systems
  • Maximum power transfer theorem optimizes power delivery to a load
  • Impedance matching techniques improve efficiency in AC circuits
• Transient power behavior occurs during circuit energizing or de-energizing
  • Involves capacitive or inductive elements
  • Can lead to temporary power spikes or dips

Voltage, Current, and Resistance

Ohm's Law and Resistance Concepts

• Ohm's Law defines relationship: $V = IR$
  • V is voltage, I is current, R is resistance
  • Governs behavior of linear electrical components
• Resistance measured in ohms (Ω)
  • Represents opposition to current flow
  • Determined by material properties and physical dimensions of conductor
• Voltage-current characteristic of resistor linear
  • Results in straight line when plotted on graph
  • Not true for all circuit elements (diodes, transistors)
• Temperature impacts resistance in many materials
  • Can lead to non-linear behavior in some circuit elements
  • Positive temperature coefficient (PTC) materials increase resistance with temperature
  • Negative temperature coefficient (NTC) materials decrease resistance with temperature

Circuit Configurations and Resistance

• Series circuits increase total resistance
  • $R_total = R_1 + R_2 + R_3 + ...$
  • Current same through all components
• Parallel circuits decrease total resistance
  • $1/R_total = 1/R_1 + 1/R_2 + 1/R_3 + ...$
  • Voltage same across all components
• Conductance (G) reciprocal of resistance
  • $G = 1/R$
  • Measured in siemens (S)
  • Useful for analyzing parallel circuits
• Conductivity reciprocal of resistivity
  • Measures material's ability to conduct current
  • Independent of physical dimensions

Current Flow in Circuits

Current Distribution and Circuit Paths

• Complete circuit path necessary for current flow
  • Open circuit prevents current flow (broken wire, open switch)
  • Short circuit provides low-resistance path (can lead to excessive current)
• Branch currents in parallel circuits divide based on resistance
  • Follow current divider principle
  • $I_1 = I_total (R_2 / (R_1 + R_2))$ for two parallel resistors
• Direction of current flow determined by:
  • Polarity of voltage source
  • Arrangement of circuit elements
• Mesh current analysis technique for solving complex circuits
  • Assigns currents to loops rather than individual branches
  • Utilizes Kirchhoff's Voltage Law equations

Transient Behavior and Advanced Concepts

• Transient current behavior occurs when circuit energized or de-energized
  • Involves capacitive or inductive elements
  • Resistors-capacitor (RC) circuits exhibit exponential voltage and current changes
  • Resistor-inductor (RL) circuits show similar behavior with current
• Norton and Thevenin equivalent circuits simplify complex network analysis
  • Norton represents circuit as current source with parallel resistance
  • Thevenin represents circuit as voltage source with series resistance
• Alternating current (AC) introduces concepts of impedance and reactance
  • Impedance combines resistance and reactance
  • Capacitive reactance decreases with frequency
  • Inductive reactance increases with frequency