How to calculate the equivalent resistance value for resistors in series? In many electrical circuits resistors are connected in series or parallel. A designer might for example combine several resistors with standard values (E-series) to reach a specific resistance value. For series connection, the current through each resistor is equal. There is only one path for the current to follow. The voltage drop however, is proportional to the resistance of each individual resistor. The equivalent resistance of several resistors in series is given by: The voltage across each resistor is calculated with Ohm’s law: Example Consider a circuit as shown in the picture below. Two resistors R1 and R2 connected in series are subject to a constant current I. How can we calculate the voltage drop for each resistor and how can we determine the equivalent resistance value for the two resistors? The current through each resistor is equal. Knowing this, and using Ohm’s law we get the voltage drop for R1 and R2: The equivalent resistance is equal to the sum of R1 and R2: This corresponds with the voltage drops that we calculated: Networks with resistors in parallel and series Take a look at the article resistors in parallel to find practical examples of how to solve a resistor network with resistors that are connected in series and parallel. The following video might help to get a quick understanding in solving resistor networks. Read more in the Resistor Guide E-Book.
How to calculate the equivalent resistance value for resistors in parallel? Resistors are often connected in series or parallel to create more complex networks. An example of 3 resistors in parallel is shown in the picture above. The voltage across resistors in parallel is the same for each resistor. The current however, is in proportion to the resistance of each individual resistor. The equivalent resistance of several resistors in parallel is given by: The current through each resistor is given by: To quickly calculate the equivalent resistance value of two resistors in parallel, you can use the parallel resistor calculator. example A circuit designer needs to install a resistor with 9 ohms and can choose from the E-12 series of preferred values(.., 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82, ..). The value of 9 ohms is unfortunately not available in this series. He decides to connect to standard values in parallel with an equivalent resistance of 9 ohms. The equivalent resistance value for 2 resistors in parallel is calculated with these steps: The above equation shows that if R1 is equal to R2 Req is half of the value of one of the two resistors. For a Req of 9 ohms, R1 and R2 should therefore have a value of 2×9=18 ohms. This happens to be a standard value from the E-series. As a solution finally, the designer connects two resistors of 18 ohms in parallel as shown in the figure right. How to solve a network with resistors in parallel and series? A more complex resistor network can be solved by systematic grouping of resistors. In the picture below three resistors are connected. Resistors R2 and R3 are connected in series. They are in parallel with resistor R1. To solve the network, the resistors [… read more]