Confusion about combining resistors in series.

[dragonkore]

Hello, everybody.

I'm reading through my EE textbook and I'm having some confusion about when to combine resistors in series. The following figure is in my book:

I see that they combine the parallel resistors of 6Ω and 3Ω to make the equivalent circuit shown in 2.42b. What I'm confused about is why they didn't then combine the 4Ω and 2Ω resistors. They do this throughout the entire chapter's examples and it's causing me confusion. Resistors are considered in series if they share the same current, correct? And the two resistors in 2.42b appear to share the same current, so I don't see why they don't combine them.

Thanks for reading.

(I apologize if this is considered homework help. It seems to be more of a general circuit question.)

 

[vk6kro]

If you only wanted to get the current from the battery, you would combine all the resistors.

However, if you wanted to get the voltage across the parallel comination, then you would have to keep that resistance separate so that you could calculate the voltage.

In fact you could do both. The combined resistance is 6 ohms (4 ohms + 2 ohms) so the current is 2 amps (12 volts / 6 ohms).

So the voltage across (a) - (b) is 4 volts. (V = i * R = 2amps * 2 ohms = 4 volts)

 

[sophiecentaur]

The volts across ab will be 2/(4+2) of the total volts. It's a 'simple' potential divider, once you have manged to combine the 6 and 3 Ohm resistors correctly (which you have). The potential divider is one of those basic circuit elements that 'everyone' should get familiar with.

 

[dragonkore]

So you can combine all of the resistors to find the current through the circuit, but you have to leave them separated if you want to find v₀. That makes sense; thanks to the both of you.

 

[alphysicist]

Hello,

Thank you for bringing up this confusion. It is important to understand the concept of resistors in series and parallel in order to accurately analyze circuits.

In this specific circuit, the 6Ω and 3Ω resistors are in parallel because they share the same two nodes and have the same voltage drop across them. When resistors are in parallel, the total resistance is calculated using the formula 1/Rt = 1/R1 + 1/R2. In this case, the equivalent resistance is 2Ω.

Now, the 4Ω and 2Ω resistors are in series because they are connected one after the other and have the same current flowing through them. When resistors are in series, the total resistance is simply the sum of the individual resistances. In this case, the equivalent resistance is 6Ω.

Combining these two equivalent resistances gives us the final equivalent resistance of 8Ω. So, in this case, the resistors are not combined because they are already in their respective equivalent forms.

I hope this helps clarify your confusion. If you have any further questions, please feel free to ask. It is always important to fully understand the concepts in order to accurately analyze and design circuits.

Best,