Electrical Circuits: Essential Concepts and Components

Posted on Feb 7, 2025 in Textile Technology and Design Engineering

1. Ohm’s and Kirchhoff’s Laws

Ohm’s Law: Defines the relationship between voltage (V), current (I), and resistance (R) in a circuit. It is expressed as:

V = IR

  • Theoretical Explanation: It shows that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance.
  • Graphical Representation: A plot of current (I) versus voltage (V) for a resistor is a straight line, indicating a linear relationship.

Kirchhoff’s Laws:

  • Kirchhoff’s Current Law (KCL): The total current entering a node equals the total current leaving the node.
  • Example Circuit: At a junction, if I1 = 3A, I2 = 2A, and I3 leaves the junction, then I3 = 5A.
  • Kirchhoff’s Voltage Law (KVL): The sum of all voltages in a closed loop equals zero: ∑V = 0.
  • Example Circuit: In a loop with a 10V source and resistors dropping 6V and 4V, KVL confirms: 10V – 6V – 4V = 0.

2. AC and DC Currents – Main Differences

  • AC (Alternating Current):
    • Definition: The current changes direction periodically.
    • Waveform: Typically sinusoidal.
    • Applications: Power transmission, household appliances.
    • Advantages: Easy to transform voltage levels, efficient for long-distance transmission.
  • DC (Direct Current):
    • Definition: The current flows in a single direction.
    • Waveform: Constant (straight line in a graph).
    • Applications: Batteries, electronics, and portable devices.
    • Advantages: Stable and suitable for electronic circuits.
  • Key Differences:
    • Direction: AC alternates periodically, DC is unidirectional.
    • Transmission: AC is efficient over distance, DC is inefficient.
    • Source Example: AC generators, DC batteries.

3. Inductor, Capacitor, and Resistor

  • Resistor:
    • Principle: Opposes the flow of current, converting electrical energy into heat.
    • Usage: Voltage division, current limitation, and signal conditioning.
  • Capacitor:
    • Principle: Stores energy in an electric field; charges and discharges over time.
    • Usage: Filtering, coupling, decoupling, and energy storage.
  • Inductor:
    • Principle: Stores energy in a magnetic field when current flows through it.
    • Usage: Energy storage, filtering in power supplies, and tuning circuits.

4. How to Minimize Pulsations in DC Circuits

Methods:

  1. Using Capacitors: Capacitors smooth voltage fluctuations by storing and releasing charge.
  2. Inductors: Inductors resist changes in current, reducing ripple in power supplies.
  3. Voltage Regulators: Linear or switching regulators stabilize the output voltage.
  4. Filters: RC or LC filters reduce high-frequency pulsations.

High Voltage and Current Cases: Use a combination of large capacitors and inductors (e.g., LC filters) to handle large power levels effectively.

5. Sine Wave Characteristics

Definition: A sine wave is a periodic waveform defined by: v(t) = Vm sin(ωt + ϕ)

Where:

  • Vm: Amplitude.
  • ω: Angular frequency (2πf).
  • ϕ: Phase angle.

Characteristics:

  1. Amplitude (Vm): Maximum value of the waveform.
  2. Frequency (f): Number of cycles per second (Hz).
  3. Period (T): Time for one complete cycle (T = 1/f).
  4. Phase: Offset of the waveform at t = 0.

6. AC Current and Phasor Diagram

  • Phasors: Represent AC quantities (voltage and current) as rotating vectors in the complex plane.
  • Phasor Diagram: Shows the phase relationship between different AC signals (e.g., voltage and current in resistive, capacitive, or inductive circuits).

7. Active, Reactive Elements, and Vector Diagram

  • Active Power (P): Real power consumed by resistive elements. P = V ⋅ I ⋅ cos(ϕ).
  • Reactive Power (Q): Power exchanged between inductive/capacitive elements. Q = V ⋅ I ⋅ sin(ϕ).
  • Apparent Power (S): Combined effect of active and reactive power. S = √(P² + Q²).
  • Vector Diagram: A graphical representation of P, Q, and S, showing phase relationships.

8. Instantaneous Values of P, V, and I in an AC Circuit

  • Instantaneous Voltage v(t): v(t) = Vm sin(ωt + ϕ).
  • Instantaneous Current i(t): i(t) = Im sin(ωt).
  • Instantaneous Power p(t): p(t) = v(t) ⋅ i(t). This oscillates at double the supply frequency.

9. Power Transformer – Primary and Secondary Windings

Definition: A power transformer transfers electrical energy between circuits using electromagnetic induction.

  • Primary Winding: Connected to the power source.
  • Secondary Winding: Delivers power to the load.
  • Turn Ratio: Vp/Vs = Np/Ns, Where Vp, Vs are primary/secondary voltages, and Np, Ns are the number of turns.

10. Examples of Simple Electrical Converters

  • Linear Regulators:
    • Advantages: Simple design, low noise.
    • Disadvantages: Inefficient for high power (wastes energy as heat).
  • Rectifiers: Convert AC to DC:
    • Advantages: Easy implementation.
    • Disadvantages: Requires additional filtering to reduce ripples.
  • Switched-Mode Power Supplies (SMPS): Higher efficiency than linear converters.

11. Types of Electronic Converters and Parameters

  1. DC-DC Converters: Step-up (boost), step-down (buck), and buck-boost converters.
  2. AC-DC Converters: Rectifiers for converting AC to DC.
  3. AC-AC Converters: Frequency changers or voltage controllers.
  4. DC-AC Converters: Inverters.
  • Adjustable Parameters: Output voltage, current limits, frequency, and efficiency.

12. Inductor Volt-Second Balance, Capacitor Charge, and Small Ripple Approximations

These principles are fundamental in the analysis and design of Switch-Mode Power Supplies (SMPS) and other power electronic circuits, ensuring steady operation and simplifying analysis.

  1. Inductor Volt-Second Balance: The volt-second balance is based on the fact that, in a steady state, the net voltage applied across an inductor over one switching period is zero. This is because the inductor cannot accumulate energy indefinitely.
  2. Capacitor Charge Balance: The charge balance principle states that, in steady state, the net charge entering or leaving a capacitor over one switching period is zero. Since capacitors store energy in the form of charge, any imbalance would lead to a change in the capacitor’s voltage over time.
  3. Small Ripple Approximation: The small ripple approximation assumes that the ripple in inductor current (ΔIL) and capacitor voltage (ΔVC) is small compared to their average values. This simplifies analysis without significant loss of accuracy.