Series and Parallel Circuits

Introduction

• Discusses series and parallel circuits with batteries and resistors.
• Resistors can be viewed as light bulbs.
• Series circuit: one path for current.
• Parallel circuit: multiple paths for current.

Circuit Characteristics

• Series Circuit:
  • One path for current.
  • Increases total resistance as more resistors are added.
  • Decreases current flow, making light bulbs dimmer.
• Parallel Circuit:
  • Multiple paths for current.
  • Voltage remains constant across all paths.
  • Total resistance decreases as more resistors are added, increasing overall current.

Current Flow

• Conventional current flows from positive to negative.
• Electrons flow from negative to positive.

Series Circuit Calculations

1. Example Problem: Two resistors in series (4Ω and 6Ω) with a 30V battery.

   • Total resistance: R_total = R1 + R2 = 10Ω.
   • Use Ohm’s law: V = IR to find current: I = V/R = 30V/10Ω = 3A.
   • Voltage drop:
     • 6Ω: V = IR = 3A * 6Ω = 18V
     • 4Ω: V = IR = 3A * 4Ω = 12V
   • Kirchhoff's Voltage Law: Sum of voltage drops equals battery voltage.

2. Power Calculations:

   • Power of battery: P = VI = 30V * 3A = 90W.
   • Resistors' power:
     • 6Ω: P = I²R = 3² * 6Ω = 54W
     • 4Ω: P = V²/R = 12²/4Ω = 36W
   • Total power absorbed equals power delivered.

Concepts of Power

• Power is work divided by time.
• 1 Watt = 1 Joule/second.
• Faster energy transfer means higher power.

Example Problem: Series Circuit with Three Resistors

• Resistors: 5Ω, 3Ω, 2Ω; Battery: 60V.
• Total resistance: R_total = 10Ω.
• Current: I = 60V/10Ω = 6A.
• Voltage drops:
  • 5Ω: 30V
  • 3Ω: 18V
  • 2Ω: 12V
• Power calculations align with Kirchhoff's law.

Parallel Circuit Calculations

1. Example Problem: Two resistors (6Ω and 8Ω) with a 24V battery.

   • Voltage across resistors is the same.
   • Current through resistors:
     • 6Ω: I = V/R = 24V/6Ω = 4A
     • 8Ω: I = V/R = 24V/8Ω = 3A
   • Total current: I_total = 4A + 3A = 7A.
   • Kirchhoff's Current Law: Current into a junction equals current out.

2. Resistance and Power in Parallel Circuits:

   • Total resistance: R_equivalent = 3.43Ω using 1/R_total = 1/R1 + 1/R2 formula.
   • Power:
     • Battery: P = VI = 24V * 7A = 168W
     • Resistors:
       • 6Ω: P = I²R = 9 * 6Ω = 54W
       • 8Ω: P = V²/R = 144/4Ω = 36W

Conclusion

• Series Circuit: Single path for current; total resistance increases with more resistors.
• Parallel Circuit: Multiple paths; voltage across resistors is the same.
• Power conservation: Power delivered equals total power absorbed by resistors.