# Series Resistors

fact

Two resistors are in series if they connect at only one point (called a node) and there is nothing else connected at that point

example

Determine whether resistors R1 and R2 below are in series.

R1 and R2 are connected at only one point and they are the only two things connected at that point so they are in series.example

Determine whether the resistors R1 and R2 below are in series.

Although they're drawn at a right angle this is the same as the example above, R1 and R2 are still in series with one another.example

Determine whether the resistors R1 and R2 below are in series.

R1 and R2 are connected at only one point but R3 is also connected to that point so none of these resistors are in series with each other.example

Determine whether the resistors R1 and R2 below are in series.

R1 and R2 are not in series since they are connected to one another at 2 locations. We call this connection "parallel" and you'll learn more about it later.example

Determine whether the resistors R1 and R2 below are in series.

R1 and R2 are in series with one another in the image above since they are connected to each other at only 1 point and nothing else is connected to that point. Even though each of them is also connected to R3; R1 and R2 are still in series.fact

If two resistors are in series we can replace them with a single "equivalent" resistor. When we do this the rest of the circuit cannot tell the difference.

fact

The resistance of the equivalent resistor is simply the sum of the two resistors in series.

example

Find the equivalent resistance of R1 and R2

R1 and R2 are in series so we can replace them with a single resistor whose resistance is \(R_{eq} = R1 + R2 = 100 + 300 = 400\Omega\) The equivalent resistor Req can be drawn instead of R1 and R2 as shown:fact

If you have three or more resistors all in series then you can combine them into a single equivalent resistor by adding their resistances, just like with two series resistors.

practice problems