In-Depth Notes on Electricity & Electronics - Circuit Theory

Learning Outcomes

• Understand and use Ohm’s Law
• Identify SI Prefixes
• Understand why we use Conventional Current
• Differentiate between DC and AC
• Identify and explain the concept of fixed resistors

Power

• Definition: The rate of energy transfer or conversion measured in Watts (W).
  Formula: P = \frac{E}{t} where:

  • P = Power (W)
  • E = Energy (J)
  • t = Time (s)

• Power Equations:

  • When current is:
  • known: P = VI where:
    • V = Voltage (V)
    • I = Current (A)
  • unknown:
    • P = \frac{V^2}{R} when voltage is known
    • P = I^2 R when current is known

International System of Units (SI)

• Common Prefixes:
  • Giga- (G): 10^9 (\rightarrow 1,000,000,000)
  • Mega- (M): 10^6 (\rightarrow 1,000,000)
  • Kilo- (k): 10^3 (\rightarrow 1000)
  • Hecto- (h): 10^2 (\rightarrow 100)
  • Deka- (da): 10^1 (\rightarrow 10)
  • Base Unit: 10^0 (\rightarrow 1)
  • Deci- (d): 10^{-1} (\rightarrow 0.1)
  • Centi- (c): 10^{-2} (\rightarrow 0.01)
  • Milli- (m): 10^{-3} (\rightarrow 0.001)
  • Micro- (μ): 10^{-6} (\rightarrow 0.000001)
  • Nano- (n): 10^{-9} (\rightarrow 0.000000001)

Direct Current (DC) vs Alternating Current (AC)

• DC: Current flows in one direction; used in batteries and electronic devices.
  • Examples: Mobile phones, electrical vehicles.
• AC: Current flows in alternating directions; used for power supply to homes and buildings.
  • AC is converted to DC in devices like TVs.

Conventional Current

• Definition: Current is considered to flow from positive to negative terminal (historical convention).
• Electron Flow: Actually flows from negative to positive terminal.

Resistors

• Function: Restrict flow of electrical charge, dissipate energy.

• Types:

  • Fixed Resistors: Maintain constant resistance.
  • Variable Resistors: Resistance can be adjusted.

• Power Dissipation in Resistor: P = I^2 R where:

  • I = Current through the resistor
  • R = Resistance

• Resistance Factors:

  • Length
  • Cross-sectional area
  • Material type

• Preferred Values: Resistors are manufactured in standard resistance values due to impracticality of endless variations.

• Colour Code: System for identifying resistor values and tolerance (0-10%).

Ohm’s Law

• Formulas:
  • V = IR
  • I = \frac{V}{R}
  • R = \frac{V}{I}
• Utilized in calculations involving current, voltage, and resistance.

Short Circuit

• Definition: Occurs when current travels along an unintended low-resistance path, potentially causing overheating and damage.

Resistors in Series

• Behavior:
  • Current remains constant through all resistors: I = I1 = I2 = … = I_n
  • Voltages add up: Vs = V1 + V2 + … + Vn
  • Total Resistance: Rs = R1 + R2 + … + Rn

Resistors in Parallel

• Behavior:
  • Voltage is the same across each resistor: Vs = V1 = V2 = … = Vn
  • Total Current: It = I1 + I2 + … + In
  • Resistance Calculation: \frac{1}{Rp} = \frac{1}{R1} + \frac{1}{R2} + … + \frac{1}{Rn}

Voltage Divider

• Definition: A circuit that divides voltage among resistors in series.
• Formula: V{out} = V{in} \times \frac{R2}{R1 + R_2}

Current Divider

• Definition: Describes how total current divides among parallel branches.
• Current through each resistor in parallel can be found using:
  • I{R1} = It \times \frac{R2}{R1 + R_2}
  • I{R2} = It \times \frac{R1}{R1 + R_2}$$