SIMPLIFIED: "10.3: Resistors in Series and Parallel"

Link to article: https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/10%3A_Direct-Current_Circuits/10.03%3A_Resistors_in_Series_and_Parallel 

Note: The image above was taken from the original article.

The article linked above talks about resistors in series and parallel, and how to calculate the equivalent resistance. This idea of calculating the equivalent resistance sounds pretty scary at first, so we are going to break down how to do that mathematically.

First, let’s define equivalent resistance. Equivalent resistance is the total amount of resistance that is in a circuit. The way to calculate equivalent resistance is different depending on if the resistors are in series vs. if the resistors are in parallel. 

Let’s start with if the resistors are in series. If resistors are in series, that means there is only ONE path for electrons to move (meaning there is only one way for current to flow). The formula to calculate equivalent resistance for resistors that are in series is very straightforward: equivalent resistance of resistors in series = resistor 1 + resistor 2 + however many resistors there are. 

However, if the resistors are in parallel, the formula is different. If resistors are in parallel, that means that there is more than one way for current to flow. When this happens, you cannot just add up the resistances of the resistors to get the equivalent resistance like you did with the resistors in series. When dealing with parallel resistors, the formula is: 

Just as a clarification, R_t stands for total resistance, which is the same thing as equivalent resistance.