the output voltage of the voltage divider shown in the picture

[parsa]

the book I'm reading,explains how to calculate the output voltage in that voltage divider shown in the picture and it says:
I=V(in)/R1+R2 then this:V(out)=IR2=(V(in)/R1+R2)×R2
I wanna know why it did this at the second calculation:  ×R2

[Le_Bassiste]

fully aware of starting a PEMDAS war right now  ,
the first equation should read I=V(in)/(R1+R2), the second one should read V(out)=I x R2=V(in)/(R1+R2)×R2.

maybe that answers your question already.
 

[ataradov]

Because you are interested in a voltage across R2 in this case.

The current over both resistors is the same, and it was calculated by the first equation. Now the second equation uses that current to calculate a voltage across the R2.

And yes, you need to be more careful writing down the equations, since as written they make no sense. But I assume it was just a simplification.

[parsa]

Because you are interested in a voltage across R2 in this case.

The current over both resistors is the same, and it was calculated by the first equation. Now the second equation uses that current to calculate a voltage across the R2.

And yes, you need to be more careful writing down the equations, since as written they make no sense. But I assume it was just a simplification.

I know that,but the current already past the R2,that's why it got used in the first equation and also how can l know I should just use the R2 to calculate the output voltage?(the image is not understandable)

[ataradov]

What do you mean by "past the R2"?  The current over both resistors is the same and depends on the value of both resistors and the voltage applied.

Your Vout arrows point to the voltage across the R2, so you use the value of R2. If you wanted the voltage across the R1, then you would use R1.

There is no abstract fixed "output voltage". You define what is the goal of the circuit and what constitutes the output. A common definition for the voltage divider is as shown on the picture, of course.

[golden_labels]

Write the Ohm’s law equation. There are three possible arrangements of it, depending on what you put on the left side. Do you see the one in which you multiply by resistance?

[parsa]

What do you mean by "past the R2"?  The current over both resistors is the same and depends on the value of both resistors and the voltage applied.

Your Vout arrows point to the voltage across the R2, so you use the value of R2. If you wanted the voltage across the R1, then you would use R1.

There is no abstract fixed "output voltage". You define what is the goal of the circuit and what constitutes the output. A common definition for the voltage divider is as shown on the picture, of course.

thank you so much man I got it😘

[Psi]

There's 3 parts to it.

You start with an input voltage Vin and an output voltage Vout.

First part is to figure out the current flow for Vin, which is through both R1 and R2 which can be though of as a single resistor of resistance (R1+R2).
So
Part 1
Amps = V / R
Amps = Vin / (R1 + R2)

Part 2 is just a law which states the current flowing between Vin + and Vin - must be the same.
So now you know that the current you calculated in Part1 is the current through R1, or through R2 since the law says they must be the same.

Part 3 is calculating the output voltage Vin.
The current flowing from Vout + to Vout -  only goes through R2.
So if we calculate the voltage across R2 this must also be the voltage across Vout
So V = I*R
Vout = (Current from part 1) * R2