Series v Parallel

Series Circuits

Definition: In a series circuit, components are connected end-to-end so that there is only one path for current to flow.

Characteristics:

• Total Resistance (R_total) increases: R_total = R₁ + R₂ + R₃ + …

• Current (I) is the same through all components: I_total = I₁ = I₂ = I₃ = …

• Voltage (V) is divided among components: V_total = V₁ + V₂ + V₃ + …

• Implications: If one component fails (e.g., a bulb burns out), the entire circuit stops working.

Parallel Circuits

• Definition: In a parallel circuit, components are connected across common points or junctions, creating multiple paths for current to flow.

• Characteristics:

  • Total Resistance (R_total) decreases: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …

  • Voltage (V) is the same across all components: V_total = V₁ = V₂ = V₃ = …

  • Current (I) is divided among components: I_total = I₁ + I₂ + I₃ + …

• Implications: If one component fails, the other components continue to operate, providing an easier and safer alternative for many electrical devices.

Key Differences

Applications

• Series circuits: Often used in string lights or for simple devices.

• Parallel circuits: Common in household wiring where devices require the same voltage and must operate independently.