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Resistors in Series

Intro​

Resistors can be placed in series (end to end), in a circuit like the following:

Diagram of a circuit showing a source voltage connected to three resistors connected in series, labeled R1, R2, and R3.

In this case, the total resistance is the sum of each resistor. So for instance, given the following resistors:

  • R1 - 100Ω
  • R2 - 5Ω
  • R3 - 1kΩ

Then the total resistance would be:

Total Resistance = 1,000Ω + 100Ω + 5Ω = 1,105Ω

Common Current, Different Voltage​

Resistors in a series share a common current, that is the amount of amps flowing through each one is the same, since there's only one path.

So for instance, given the previously calculated resistance of 1,105Ω, if we were to supply 5V of electrical force, we can use Ohm's law to calculate the current at any given point as:

I = 5V / 1,105Ω = 0.004A = 4mA

So no matter where in the circuit that we measure the current, we would get the same value of 4mA:

Diagram of a circuit showing a source voltage connected to three resistors connected in series, labeled with 100 ohms, 5 ohms, and 1 kiloohm.

Power Calculation​

Given that we know the current and resistance at any resistor in a series, we can use the P = I^2 * R form of the power law we derived earlier from Ohm's law and the definition of the watt. However, since there are multiple resistors in the series, we add an n to specific power and resistance at resistor number n:

Pn = I^2 * Rn

Voltage Division​

Although the current at any given point in a series circuit is the same, the voltage drops as it passes through each component as the electromagnetic force is resisted. Because of this, resistances in series forms the fundamental circuit for voltage division, which we're going to explore more thoroughly in part 5 of this tutorial.

Advantages and Disadvantages of Series Resistors​

Because series resistance is simply the sum of each of the individual resistances, stringing resistors together end to end allows for a specific resistance to be built using various combinations of individual resistors. This can be especially useful when using spare parts for prototyping.

A disadvantage of series resistance is that if one resistor fails open (no longer conducting current across it), the whole series circuit will also fail open. If the resistor fails as a short (it no longer provides resistance, but becomes a conductor), the totality of resistance in the series will be lowered by its amount of resistance.

Because there's little advantage to a series resistor network in terms of pure resistance, usually resistors in series are used in circuits to divide voltage.

Next - Parallel Resistance​