Lecture Notes: Circuits

Key Topics:

• Voltage, Current, Resistance
• Ohm’s Law
• Series and Parallel Circuits
• Voltage, Current, and Power Relations
• Kirchhoff’s Laws
• AC vs DC Current

Basic Concepts:

Voltage, Current, and Resistance

• Voltage (V): Energy per unit charge, measured in Volts (V)
• Current (I): Rate of flow of charge, measured in Amperes (A)
• Resistance (R): Opposition to current flow, measured in Ohms (Ω)

Ohm’s Law

• Formula: V = I * R
• Application: To find any of the three variables if the other two are known*

Series vs Parallel Circuits

• Series: Current is the same through all components, voltages add up
• Parallel: Voltage is the same across all components, currents add up

Detailed Analysis:

Calculating Current

Example:

• Given: Battery = 12V, Resistor = 3Ω
• Use Ohm’s Law: I = V/R = 12V/3Ω = 4A
• Current flows from positive to negative terminal of the battery

Effect of Voltage and Resistance on Current

• Increasing Voltage: Increases current (Direct Relation)
• Increasing Resistance: Decreases current (Inverse Relation)

Definitions:

• Voltage: Energy (Joules) per charge (Coulombs)
• Current: Charge (Coulombs) per time (seconds)
• Power (P): Rate of energy transfer, measured in Watts (W)
  • Formulas:
    • P = VI
    • P = I²R
    • P = V²/R

Work and Energy

• Work (W) is measured in Joules
• Formula: W = -Q * ΔV*

Advanced Concepts:

Kirchhoff’s Laws

• Voltage Law: The sum of all voltages around a closed loop equals zero
• Current Law: The total current entering a junction equals the total current leaving

Calculating Electrons

• Formula: Q = I * T
• Example: Convert charge to number of electrons using the charge of one electron*

Series and Parallel Calculations

Series:

• Total Resistance (Rₜ): Sum of individual resistances
• Total Current (Iₜ): Same through each resistor
• Voltage Drop: V = IR for each resistor

Parallel:

• Total Resistance (Rₜ): 1/Rₜ = 1/R₁ + 1/R₂
• Total Current (Iₜ): Sum of currents through each path

Power in Circuits

• Battery Power: P = VI
• Resistor Power Absorption: Calculated using P = I²R or P = V²/R

Circuit Examples:

Series Circuit Example

• Total Resistance: Add resistances
• Calculate Current: Total voltage / Total Resistance
• Voltage Across Each Resistor: Use V = IR

Parallel Circuit Example

• Calculate Current Through Each Resistor: V/R for each
• Total Current: Sum of individual currents

Combination Circuits

• Simplify using series or parallel formulas
• Calculate equivalent resistance, current, and voltage drops

Voltage Divider

• Formula: Vout = (R2 / (R1 + R2)) * Vin
• Used to get desired voltage drop across a component*

Measurement Devices:

Ammeters and Voltmeters

• Ammeter: Connected in series, low internal resistance
• Voltmeter: Connected in parallel, high internal resistance

AC vs DC Current

• DC (Direct Current): Flows in one direction
• AC (Alternating Current): Changes direction periodically
• Frequency: Measured in Hertz (Hz), affects AC current direction changes

These notes summarize the key points and calculations discussed in the lecture on circuits, providing a comprehensive overview of fundamental and advanced concepts in electrical circuits.