Solving for Req in a Series Circuit - Understanding Resistors and Voltage

[J.live]

Homework Statement

Solve for Req

The Attempt at a Solution

The resistors in the middle can be added to total of 5 ohms. So then then 5v +5ohms = 10 ohms

Then they are all in series 1.5+10+ 1.5= 12.5? What I don't understand is what do i do with
Rx? or 12.5 is Req?

Here is the circuit:

 

[xcvxcvvc]

hmm. just an fyi: i don't see any circuit beneath your promise for the circuit

 

[J.live]

Sorry about that.

 

[xcvxcvvc]

you are correct that the middle branch can be replaced with 5 ohms. However, it does not add in series with the other 5 ohm resistor to its right. instead, they add in parallel. Then that parallel combination adds in series with the 1.5 and 1 ohm resistors.

 

[DeeNos]

In a series circuit, the equivalent resistance (Req) is equal to the sum of all the individual resistances. In this case, we have three resistors: 1.5 ohms, 5 ohms, and 1.5 ohms. So, Req = 1.5 ohms + 5 ohms + 1.5 ohms = 8 ohms.

To understand this concept, imagine a water pipe with three sections of different widths. The total resistance to the flow of water would be equal to the sum of the individual resistances of each section. In the same way, the total resistance in a series circuit is equal to the sum of the individual resistances.

Now, to solve for Rx, we can use Ohm's Law, which states that voltage (V) is equal to current (I) multiplied by resistance (R). So, we can rearrange this equation to solve for resistance: R = V/I. In this case, we know the voltage (5V) and the total resistance (8 ohms), so we can solve for the current using Ohm's Law: I = V/R = 5V/8 ohms = 0.625 amps.

Now, to find the resistance of Rx, we can use Ohm's Law again: Rx = V/I = 5V/0.625 amps = 8 ohms.

So, the equivalent resistance (Req) in this series circuit is 8 ohms, and the resistance of Rx is also 8 ohms. This means that the total current (I) in the circuit is 0.625 amps, and the voltage drop across each resistor is proportional to its individual resistance. This understanding of series circuits is crucial for understanding more complex circuits and for designing and troubleshooting electrical systems.