Lecture Notes: DC Circuits and Resistors

Introduction

• Importance of DC circuits in troubleshooting and building electrical systems.
• Focus on voltage, resistance, current, and resistor combinations.
• Use of practical examples to illustrate concepts.

Basics of DC Circuits

• DC circuit: Current flows in one direction through a closed loop.
• Simplest circuit components:
  • Voltage source (e.g., battery)
  • Connecting wires
  • Resistor (e.g., light bulb)
• Voltage: Creates potential difference, driving current.
• Current: Flow of electric charge, conventionally described as moving from positive to negative terminal.
• Ohm’s Law: Current ( I = \frac{V}{R} )

Example 1: Calculating Current

• Given: Battery = 1.5 V, Resistor = 150 ohms
• Current ( I = \frac{1.5 \text{ V}}{150 \text{ ohms}} = 0.01 \text{ A} = 10 \text{ mA} )

Resistor Configurations

• Series Configuration:

  • Resistors connected end-to-end.
  • Total Resistance ( R_{total} = R_1 + R_2 + \ldots )
  • Example: 5 ohms + 10 ohms + 15 ohms = 30 ohms.
  • Current is the same through all resistors.

• Parallel Configuration:

  • Resistors provide multiple paths for current.
  • Total Resistance using reciprocal formula.
  • Example: ( \frac{1}{R_{total}} = \frac{1}{6} + \frac{1}{12} = \frac{1}{4} )
  • Voltage is the same across all resistors.

Mixed Circuits

• Combination of series and parallel resistors.
• Simplification by reducing series and parallel combinations.
• Example 2:
  • Two 10 ohm resistors in parallel: Equivalent resistance = 5 ohms.
  • In series with a 20 ohm resistor: Total resistance = 25 ohms.
  • Current with 12 V battery: ( \frac{12 \text{ V}}{25 \text{ ohms}} = 0.48 \text{ A} )

Power in Circuits

• Power dissipation as heat: ( P = I^2 R )
• Example 3:
  • 5 ohm resistor, 2 A current: ( P = 2^2 \times 5 = 20 \text{ W} )
  • Energy over time: ( E = P \times \text{time} )
  • For 10 seconds: ( E = 20 \times 10 = 200 \text{ J} )

Practical Applications

• Resistors in voltage dividers, current limiting, and heat dissipation.
• Example 4:
  • 100 ohm resistor with 9 V battery: ( P = \frac{9^2}{100} = 8 \text{ W} )

Advanced Concepts

• Analyzing complex circuits with multiple branches and voltage sources.
• Series and parallel reduction for solving equivalent resistance, current, and voltage.

Practice Challenge

• Circuit with 10 ohm and 20 ohm resistors in parallel, in series with 30 ohm resistor.
• Parallel combination: Approx. 6.67 ohms.
• Total resistance: 36.67 ohms.
• Current with 12 V battery: ( \frac{12 \text{ V}}{36.67 \text{ ohms}} \approx 0.33 \text{ A} )

Conclusion

• Understanding DC circuits principles aids in tackling electrical challenges.
• Encouragement to explore further for deeper insights and practice.