ITE Slide4(StudyNotes)

INTRODUCTION TO ELECTRONICS (GTGE 121) LECTURE 3

Open and Short Circuits

• The most common problems (faults) in circuits are open circuits and shorts.

• A short circuit in all or part of a circuit causes excessive current flow.

  • This may blow a fuse or burn out a component, which may result in an open-circuit condition.

• An open circuit represents a break in the circuit, preventing current from flowing.

• Short circuits may be caused by various factors such as:

  • Wire crossing

  • Insulation failure

  • Solder splatter inadvertently linking two separate conductors within a circuit board.

• An open circuit may result from:

  • Wire or component lead separation from the circuit

  • A component that has simply burned out, resulting in a huge resistance.

• A fuse is used in the circuit and will blow when the current through it exceeds its current rating, given in amps.

Example Circuit Conditions

• Example Circuit Scenarios:

  • Normal Circuit: With a current flow denoted as 1 = 0.91A, resistance R = 1.0Ω, total voltage = 10V.

  • Open Circuit: Conditions leading to an open circuit scenario are shown in Figure 2.59.

  • Short Circuit: Results in current = 10A, resistance approaches zero, and fuse blows.

Short Circuit Characteristics

• A key characteristic of a short circuit is:

  • If considering all components as ideal, infinite current will flow if an ideal voltage source is short-circuited, leading the voltage across the short to zero.

• Real voltage sources and conductors have internal resistance, limiting the maximum current.

  • Nevertheless, there's usually enough current to cause damage.

• Possible symptoms of a short circuit include:

  • A burning smell

  • Overheating components.

Circuit Protection Devices

• To prevent short circuits from causing damage, various protection devices can be employed, such as:

  • Fuses

  • Transient voltage suppressors

  • Circuit breakers.

• These devices sense excessive current flow and will either blow or trip, creating an open-circuit condition to limit damage.

Examples of Current Flow in Circuits

Example 1: Series Circuit (Fig. 2.60)

• Calculate current flows in three scenarios:

  • Normal Circuit: 11 mA

  • Partial Short Circuit: 109 mA

  • Full Short Circuit: 4 A (fuse blows).

Example 2: Parallel Circuit (Fig. 2.61)

• Determine total current flow for different circuit conditions:

  • Normal Circuit: 3.4 A

  • Open Circuit: 2.3 A

  • Short Circuit: 6 A (fuse blows).

Example 3: Load Behavior (Fig. 2.62)

• When switch S2 is closed, loads B, C, and D receive no power, while load A does. If the fuse is blown, replacing it leads to:

  • Closing S2 without resetting the conditions works.

  • Close S3 powers B and C with no effect.

  • Closing S4 cuts power to B and C, leading to a blown fuse again.

• Diagnosis: Load D has a short in it.

Kirchhoff’s Laws

• Suitable for analyzing complex circuits that can't be simplified using resistor reduction alone, especially those with multiple sources.

• Kirchhoff's laws work for both linear and nonlinear circuit elements, offering a universal method.

Kirchhoff’s Voltage Law

• States that the total sum of electrical potential differences around any closed circuit must equal zero:
  $\Sigma V = 0$

• Application example shown in Fig. 2.63 involves tracing a loop from a battery.

• The equation formed can be complicated by nonlinear components but ultimately demonstrates the laws' universality.

• Voltage changes across capacitors and inductors yield complex expressions, yet they adhere to Kirchhoff’s principles.

Kirchhoff's Current Law (Junction Rule)

• States that the sum of currents entering a junction equals the sum leaving it:
  $\Sigma I_{in} = \Sigma I_{out}$

• This reflects charge conservation in a circuit.

Application of Kirchhoff's Laws

• Example: Use Kirchhoff’s laws to solve for unknown currents (i1, i2, …, i6) and subsequent voltage drops across resistors.

• Apply Kirchhoff's law to generate required equations through loops and junctions for solving.

AC Circuits

• Definition of a circuit: A complete conductive path for electron flow from source to load and back.

• Direct Current (DC): Current flows in one direction.

• Alternating Current (AC): Current periodically changes direction.

  • Voltage also reverses periodically.

• AC voltage and current can be represented by sinusoidal waveforms generated by alternating sources, frequently varying in frequency from few hertz to billions of hertz.

Generator Mechanics

• AC Generators: Use electromagnetic induction to create sinusoidal waveforms, typically involving a rotating coil in a magnetic field.

  • Proportional to magnetic flux change.

  • Induced voltage follows sinusoidal pattern, characterized by angular frequency:
    $V = NAB \frac{dφ}{dt}$

Why AC is Important

• Easily converts mechanical motion into electrical current via AC generators.

• Differentiating or integrating a sinusoidal yields sinusoidal results.

• A transformer can efficiently increase or decrease voltage without significant power losses, unlike DC systems.

Pulsating DC

• Definition: DC that varies periodically but never changes direction (Fig. 2.80).

• Could be intermixed with AC currents for analysis using specialized circuits.

Combining Sinusoidal Sources

• Sum of two AC sources can produce complex waveforms, exhibiting phenomena such as beats when near-frequency sources combine.

AC Waveforms

• Alternating currents can take on various forms:

  • Square waves are crucial in digital electronics.

  • Triangular and ramp waveforms are used for timing circuits.

Ideal DC Sources

• An ideal DC voltage source maintains fixed voltage across its terminals, whereas an ideal current source does the same for current, independent of load.

Describing AC Waveforms

• AC waveform description involves amplitude, frequency, and phase.

• Complete cycles yield frequency (Hz) as a measure of time.

• The period (T) is the inverse of frequency:
  $T = \frac{1}{f}$

Measuring Frequency and Period

• Example calculation of period from frequency for AC cycles:

  • Frequency (60 Hz): T = 1/60 = 0.0167 s.

  • Frequency of period (2 ns): f = 1/(2×10⁻⁹) = 500 MHz.

Phase Measurements

• Events measured on AC graphs, referencing cycles and phase differences in degrees.

AC Properties

• Relationships exist between RMS (root mean square) values for voltage, current, and power in both resistive and complex circuits.

Measuring RMS Values

• Digital multimeters vary in methods for reading voltages; true RMS meters are essential for nonsinusoidal inputs.

• Accurate RMS determination possible through calculations based on known circuit parameters, like peak values.

Examples of Electrical Calculations

• Numerous examples given that illustrate Ohm’s law under AC conditions, including power dissipated across resistors of varying resistance values when subjected to a given AC voltage.