Resistor Circuits

Resistors in Series

When resistors are connected end-to-end, they are said to be connected in series. In a series circuit there is only one path for current to flow, so the same current passes through every resistor. Series resistor circuits are widely used in voltage dividers, LED current limiting, sensor circuits, battery packs and many other electronic applications.

Resistors Connected in Series

What Is a Series Connection?

A series connection joins resistors one after another so that the current must pass through each resistor in turn.

Because there is only one current path, every resistor carries exactly the same current.

Characteristics of Series Circuits

  • Only one path exists for current.
  • The same current flows through every resistor.
  • The supply voltage is divided across the resistors.
  • Total resistance equals the sum of all resistors.
  • If one resistor becomes open circuit, current stops everywhere in the circuit.

Total Resistance Formula

The total resistance is simply the sum of all resistor values. 

RT = R1 + R2 + R3 + ... + Rn
Symbol Meaning
RT Total resistance.
R1, R2, R3... Individual resistor values.

Example 1 – Calculating Total Resistance

Three resistors are connected in series:

  • 100 Ω
  • 220 Ω
  • 680 Ω
RT = 100 + 220 + 680

RT = 1000 Ω

RT = 1 kΩ

Current in a Series Circuit

The current is identical through every resistor. 

I = V ÷ RT

Example: 

Supply Voltage = 12 V

Total Resistance = 1 kΩ

I = 12 ÷ 1000

I = 0.012 A

I = 12 mA

Voltage Drop Across Each Resistor

Each resistor produces a voltage drop proportional to its resistance. 

V = I × R
Resistor Voltage Drop
100 Ω 1.2 V
220 Ω 2.64 V
680 Ω 8.16 V
Total 12 V

Power Dissipation

Each resistor dissipates power according to: 

P = I² × R

The resistor with the highest resistance usually dissipates the greatest power because the current is the same through all resistors.

Practical Applications

  • LED current-limiting circuits.
  • Voltage dividers.
  • Battery balancing circuits.
  • Current sensing.
  • Power supply circuits.
  • Audio attenuators.
  • Bias networks.
  • Sensor interfaces.

Advantages

  • Simple circuit design.
  • Easy to calculate.
  • Current is identical through all components.
  • Resistance values can be increased easily.
  • Useful for voltage division.

Disadvantages

  • If one resistor fails open circuit, the entire circuit stops working.
  • The same current must pass through every component.
  • Voltage is divided among the resistors.
  • Not suitable when different currents are required.

Common Mistakes

Mistake Explanation
Adding voltages instead of resistances. Only resistor values are added to calculate total resistance.
Assuming voltage is the same across every resistor. Only the current is identical in a series circuit.
Ignoring resistor power ratings. Each resistor must safely dissipate its own power.
Using the wrong current value. The current is determined by the total resistance.

Real-World Examples

Application Series Resistors Used For
LED Indicator Current limiting.
High-Voltage Divider Sharing voltage across several resistors.
Power Supply Bleeder resistor networks.
Audio Amplifier Bias and feedback circuits.
Battery Pack Voltage sensing networks.

Key Points

  • Series resistors are connected end-to-end.
  • The same current flows through every resistor.
  • Total resistance equals the sum of all resistor values.
  • The supply voltage is divided across the resistors.
  • Series circuits are widely used in electronic design.

Next Lesson

Continue by learning about Resistors in Parallel, where the voltage is the same across every resistor while the current divides between the branches.

Next Lesson → Resistors in Parallel