Chapter 6: Series Circuits

 

Characteristics of a Series Circuit

A series circuit is one in which all components are connected end-to-end in a single path, so the same current flows through each component. There is only one path for current flow. If any component fails open (breaks), the entire circuit stops conducting.

The key properties of a series circuit are: (1) Current is the same through all components: I_T = I₁ = I₂ = I₃ = ... (2) Total resistance is the sum of all individual resistances: R_T = R₁ + R₂ + R₃ + ... (3) Total voltage equals the sum of individual voltage drops (Kirchhoff's Voltage Law): V_T = V₁ + V₂ + V₃ + ...

 

Voltage Divider Principle

One of the most practically important properties of a series circuit is the voltage divider. When resistors are connected in series across a voltage source, the voltage distributes across each resistor in proportion to its resistance value.

The voltage divider formula: V_X = V_T × (R_X / R_T) where V_X is the voltage across resistor R_X and R_T is the total series resistance. This principle is used extensively in sensor circuits, reference voltage generation, and signal conditioning.

Example: Two resistors, 10 kΩ and 20 kΩ, in series across 12V. The voltage across the 20 kΩ resistor = 12 × (20k / 30k) = 8V

 

Practical Applications of Series Circuits

Series circuits are used for current-limiting (a series resistor limits current through an LED), fuse protection (a fuse in series breaks the circuit on overcurrent), voltage division, and battery configurations (cells in series add their voltages). Christmas lights using older technology wired all bulbs in series — the characteristic that caused one blown bulb to darken the entire string.