# Replacing resistors with equivalent resistor

This is somewhat a homework assignment, but please bear with me. Given the following schematic, I want to know the overall resistance when measured from node A to node B.

simulate this circuit – Schematic created using CircuitLab

First of all, I'm not sure whether the order of calculations is important. Here's what I did: R3 and R4 are in series, so they add up to 500 Ohm. R2 is in parallel to those two, so (1/500+1/500)^-1 = 250 Ohm. Now I add R1 and my previous result because they are in series and thus get 1250 Ohm.

Is this way of calculating correct? If I, for example, first calculate R2 and R3 in parallel, and then in series with R4, I get a completely different result, which confuses me a lot.

• +1 If only all homework questions were as well-stated. Commented Aug 28, 2013 at 1:01
• The way you did it is correct. And no, you cant switch the order. R2 and R3 are not in parallel by themselves, R3 and R4 are in series with one another and together they are in parallel with R2. If you pretend R2 and R3 are in parallel, how do you factor in R4? Its in series with R3 but not with R2. Commented Jul 26, 2017 at 22:51

The first calculation you did is correct, R3 and R4 are in series, the combination is in parallel with R2 and when combined it is in series with R1.

The second method of trying to combine R3 and R2 in parallel results in an incorrect answer because they are not in parallel. Devices are in parallel if they have the same voltage across them. The voltage across R2 is split between R4 and R3, thus the voltage across R2 and R3 is not the same, which means they are not parallel.

The second calculation is wrong because that R3 is NOT in parallel with R2.

A component is considered to be in parallel with another component only if you can say that different currents flows through them.
(Not necessarily a different value, both currents may have the same exact value, but you define it as a different current because that it's in a different branch.)

R2 and R3 are not in parallel. Two resistors are in parallel only if they connect to the same two nodes.

Similarly, two resistors are in series only if they are the only two elements connecting to a single central node.

The initial calculation steps you described are correct.

Hint:

You need to do this in stages

R3 and R4 are in series so you can replace them one resistor R5

$$R5 = R3 + R4 = 500 \Omega$$

Now: R2 and the new R5 are in parallel so you replace them with R6

$$R6 = \frac{R2 \times R5}{R2 + R5} = 250 \Omega$$

There is one more step to get the final answer is R1 and the new R6 a series or parallel circuit?

It may help to redraw the circuit at each stage until you get used to simplifying this type of circuit in your head.