Electrical Fundamentals and Circuit Analysis

Electrical Fundamentals

• Basic Concepts

  • Voltage (V): Electrical potential difference, measured in volts (V).
  • Current (I): Flow of electric charge, measured in amperes (A).
  • Resistance (R): Opposition to current flow, measured in ohms (Ω).
  • Power (P): Rate of doing work or energy transfer, measured in watts (W); P = V × I.

• Ohm's Law

  • Relationship between voltage, current, and resistance: V = I × R.
  • Used to calculate one of the three variables when the other two are known.

• Circuit Components

  • Resistors: Limit current flow, dissipate energy as heat.
  • Capacitors: Store electrical energy temporarily.
  • Inductors: Store energy in a magnetic field when current flows.
  • Diodes: Allow current to flow in one direction only.
  • Transistors: Semiconductor devices used to amplify or switch electronic signals.

Circuit Analysis

• Series Circuits

  • Components connected end-to-end; same current flows through all components.
  • Total resistance: R_total = R1 + R2 + R3 + ...
  • Voltage division: V_total = V1 + V2 + V3 + ...

• Parallel Circuits

  • Components connected across the same voltage source; voltage is the same across all components.
  • Total resistance: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
  • Current division: I_total = I1 + I2 + I3 + ...

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

• Direct Current (DC)

  • Flows in one direction; constant voltage.
  • Common in batteries and electronic devices.

• Alternating Current (AC)

  • Voltage and current vary over time; typically sinusoidal.
  • Used in household power systems.

Electrical Safety

• Safety Precautions
  • Always use insulated tools.
  • Avoid wet conditions when working with electricity.
  • Use circuit breakers and fuses to prevent overloads.
  • Follow proper grounding techniques to prevent electric shock.

Measurements and Instruments

• Multimeter

  • Used to measure voltage, current, and resistance.
  • Can be digital or analog.

• Oscilloscope

  • Visualizes electrical signals over time.
  • Useful for observing waveforms and signal behavior.

Fundamental Theorems

• Superposition Theorem

  • In linear circuits, the voltage or current can be calculated by considering one independent source at a time.

• Thevenin's Theorem

  • Any linear circuit can be simplified to a single voltage source and series resistance.

• Norton’s Theorem

  • Any linear circuit can be simplified to a single current source and parallel resistance.

Basic Electrical Units

• Voltage (V): Volt (V)
• Current (I): Ampere (A)
• Resistance (R): Ohm (Ω)
• Power (P): Watt (W)
• Capacitance (C): Farad (F)
• Inductance (L): Henry (H)

Key Formulas

• Power: P = V × I
• Series Resistance: R_total = R1 + R2 + R3 + ...
• Parallel Resistance: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
• Energy (in joules): E = P × t (where t is time in seconds)

Electrical Fundamentals

• Voltage (V): The difference in electrical potential, with units in volts (V).
• Current (I): The rate of flow of electric charge, expressed in amperes (A).
• Resistance (R): The opposition to current flow, measured in ohms (Ω).
• Power (P): The rate at which work is done or energy is transferred, measured in watts (W), calculated as P = V × I.

Ohm's Law

• Describes the relationship between voltage, current, and resistance: V = I × R.
• Enables calculation of any one variable when the other two are known.

Circuit Components

• Resistors: Control and limit electric current, converting energy into heat.
• Capacitors: Temporarily store electrical energy for later use.
• Inductors: Store energy in a magnetic field during current flow.
• Diodes: Allow current to flow unidirectionally, acting as a one-way gate.
• Transistors: Semiconductor devices for amplifying or switching electronic signals.

Circuit Analysis

• Series Circuits: Components are connected end-to-end, resulting in the same current throughout.

  • Total resistance formula: R_total = R1 + R2 + R3 + ...
  • Voltage distribution formula: V_total = V1 + V2 + V3 + ...

• Parallel Circuits: Components connected across a common voltage source, maintaining the same voltage across all.

  • Total resistance formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
  • Current distribution formula: I_total = I1 + I2 + I3 + ...

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

• Direct Current (DC): Flows in one direction with a constant voltage, commonly seen in batteries.
• Alternating Current (AC): Voltage and current fluctuate over time, typically in a sinusoidal wave; standard in household power systems.

Electrical Safety

• Use insulated tools to prevent accidental electric shock.
• Avoid handling electrical equipment in wet conditions.
• Utilize circuit breakers and fuses to prevent electrical overloads.
• Adhere to proper grounding techniques to enhance safety.

Measurements and Instruments

• Multimeter: A device for measuring voltage, current, and resistance, available in digital or analog formats.
• Oscilloscope: Displays electrical signals over time, useful for analyzing waveforms and signal behavior.

Fundamental Theorems

• Superposition Theorem: In linear circuits, the effect of multiple sources can be analyzed by considering one independent source at a time.
• Thevenin's Theorem: Any linear circuit can be represented as a single voltage source in series with a resistance.
• Norton’s Theorem: Any linear circuit can be simplified to a single current source in parallel with a resistance.

Basic Electrical Units

• Voltage (V) = Volt (V)
• Current (I) = Ampere (A)
• Resistance (R) = Ohm (Ω)
• Power (P) = Watt (W)
• Capacitance (C) = Farad (F)
• Inductance (L) = Henry (H)

Key Formulas

• Power: P = V × I
• Series Resistance: R_total = R1 + R2 + R3 + ...
• Parallel Resistance: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
• Energy: E = P × t, where t is time in seconds.