What Are Resistors in Series?

Resistors are connected in series when the same current flows through each resistor one after another.

      R1          R2          R3
+───/\/\/\──────/\/\/\──────/\/\/\───−
│                                      │
└──────────────────────────────────────┘

The total resistance is the sum of all individual resistances.

Series Resistance Formula

Rtotal = R1 + R2 + R3 + ... + Rn

For example:

R1 = 100 Ω
R2 = 220 Ω
R3 = 330 Ω

Rtotal = 100 + 220 + 330

Rtotal = 650 Ω

Series Resistor Calculator

Current in a Series Circuit

The same current flows through every resistor in a series circuit.

I = Vtotal / Rtotal

Once the total resistance is known, the circuit current can be calculated if the supply voltage is known.

Series Circuit Current Calculator

Voltage Drop Across Each Resistor

Because the same current flows through every resistor, the voltage across each resistor can be calculated using Ohm's law:

V = I × R

Therefore:

V1 = I × R1

V2 = I × R2

V3 = I × R3

The individual voltage drops add up to the total supply voltage.

Voltage Drop Calculator

Power Dissipation

Each resistor dissipates power according to:

P = I² × R

The total power consumed by the series resistor network is:

Ptotal = I² × Rtotal

The sum of the individual resistor powers equals the total circuit power.

Series Resistor Power Calculator

Example — Three Resistors in Series

Suppose three resistors are connected to a 12 V supply:

R1 = 100 Ω

R2 = 220 Ω

R3 = 330 Ω

The total resistance is:

Rtotal = 100 + 220 + 330

Rtotal = 650 Ω

The circuit current is:

I = 12 / 650

I ≈ 0.01846 A

I ≈ 18.46 mA

The voltage drops are approximately:

V1 = 18.46 mA × 100 Ω
   ≈ 1.846 V

V2 = 18.46 mA × 220 Ω
   ≈ 4.062 V

V3 = 18.46 mA × 330 Ω
   ≈ 6.092 V

The voltage drops add up to approximately 12 V.

Resistors With Equal Values

If all resistors have the same resistance, the total resistance is:

Rtotal = n × R

For example, four 1 kΩ resistors in series produce:

Rtotal = 4 × 1 kΩ

Rtotal = 4 kΩ

Voltage Division Using Series Resistors

A series resistor network can be used as a voltage divider when the output voltage is taken from a resistor junction.

Vin
 │
 R1
 │
 ├──── Vout
 │
 R2
 │
GND

For a two-resistor divider:

Vout = Vin × R2 / (R1 + R2)

The resistor-divider circuit should not be confused with a series resistor network used simply to increase total resistance.

Finding a Required Series Resistance

Series resistors can be used when a required resistance value is not available as a single resistor.

For example, if 2.7 kΩ is required, several standard values can be combined:

2.2 kΩ + 470 Ω + 30 Ω

= 2.7 kΩ

The individual resistor tolerances should be considered when precision is important.

Using Series Resistors for Higher Power

Several resistors can sometimes be connected in series to distribute power dissipation.

For example, instead of using one resistor that must dissipate a large amount of power, multiple resistors can share the total voltage drop and power.

However, each resistor must still be selected for its individual voltage, power and temperature limits.

Resistor Voltage Rating

Power rating is not the only consideration when using resistors in series.

At high voltages, the voltage across an individual resistor may exceed its rated working voltage even if its power dissipation is within limits.

Check both the resistor power rating and maximum working voltage when designing high-voltage circuits.

Advantages of Series Resistors

• Simple way to increase total resistance.
• Useful for voltage division.
• Can distribute power across multiple resistors.
• Can create resistance values that are not available as a single resistor.
• The same current flows through every resistor.

Disadvantages of Series Resistors

• Total voltage is distributed between the resistors.
• Failure of one resistor can interrupt the entire circuit.
• Total resistance increases with every added resistor.
• Resistor tolerances accumulate in the total resistance.
• High-voltage applications require attention to individual resistor voltage ratings.

Common Applications

• Voltage dividers
• LED current limiting
• Transistor bias networks
• Pull-up and pull-down networks
• RC timing circuits
• Signal attenuation
• High-voltage resistor networks
• Power dissipation networks
• Creating non-standard resistance values

Common Mistakes

• Adding resistances incorrectly.
• Forgetting that the same current flows through every series resistor.
• Ignoring individual resistor power dissipation.
• Ignoring individual resistor voltage ratings.
• Using a resistor with an insufficient power rating.
• Forgetting resistor tolerance.

Key Points

• Series resistances simply add together.
• The same current flows through every resistor.
• Voltage divides according to each resistor's resistance.
• Power is dissipated by every resistor.
• Total power equals the sum of the individual resistor powers.
• Several resistors can be used to obtain a required resistance value.
• Series resistors can distribute power and voltage.
• High-voltage circuits require attention to resistor working-voltage ratings.