Circuit Analysis Lecture: Ohm's Law

Introduction

• Key Topic: Ohm's Law is fundamental to understanding electric circuits.
• Components:
  • Current: Flow of electricity in the circuit.
  • Voltage: The force pushing the current.
  • Resistance: The obstacle slowing the current flow.

Ohm's Law

• Formula: ( V = IR )
  • ( V ) = Voltage
  • ( I ) = Current
  • ( R ) = Resistance
• Concept: Voltage across an element in a circuit equals the current through it times its resistance.
• Applications: Applies to all resistors and elements in a circuit.

Algebraic Manipulations

• Current Calculation: ( I = \frac{V}{R} )
• Resistance Calculation: ( R = \frac{V}{I} )

Circuit Examples

Simple Circuit

1. Single Resistor Circuit

   • Voltage Source: 10 volts
   • Resistance: 5 ohms
   • Current Calculation: ( I = \frac{10}{5} = 2 ) amps

2. Increased Resistance

   • Resistance: 10 ohms
   • Current Calculation: ( I = \frac{10}{10} = 1 ) amp

3. Further Increased Resistance

   • Resistance: 20 ohms
   • Current Calculation: ( I = \frac{10}{20} = 0.5 ) amps

Variation in Voltage and Resistance

• Voltage Source: 1 volt
• Resistance: 50 ohms
• Current Calculation: ( I = \frac{1}{50} = 0.02 ) amps or 20 milliamps

Using Millivolts and Milliamps

• Voltage: 50 millivolts
• Current: 10 milliamps
• Resistance Calculation: Convert to volts and amps before using ( V = IR )

Series Circuits

• Example Circuit:

  • Source Voltage: 12 volts
  • Resistors: 1 ohm and 2 ohms in series
  • Current: 4 amps

• Voltage Drops Across Resistors:

  • ( V_1 = I \times R_1 = 4 \times 1 = 4 ) volts
  • ( V_2 = I \times R_2 = 4 \times 2 = 8 ) volts
  • Total voltage drop across both resistors adds up to the source voltage: ( 4 + 8 = 12 ) volts

Important Concepts

• Voltage Divider: In a series circuit, the total voltage is divided across resistors proportionally.
• Practical Applications: Voltage dividers can be used to supply different voltages to different parts of a circuit.

Conclusion

• Understanding Ohm's Law is crucial for analyzing and solving circuit problems.
• Always ensure you work within base units (volts, ohms, amps) to avoid calculation errors.
• Concepts like voltage division and series circuits form the foundation for more complex circuit analysis techniques.
• Practice is vital to mastering circuit analysis and becoming comfortable with methods like node voltage and mesh current analysis.