Engineering Calculate voltage and position of the slider

[Edy56]

Homework Statement

A total resistance potentiometer is used in the circuit in Figure 1
R POT = 10 kΩ which changes linearly from position 0 to position 1. If R= 5 kΩ, VCC= 5 V, determine:
(a) voltage value V OUT when the slider of the potentiometer is in position 0.5;
(b) position the potentiometer slider so that V OUT= 3 V.

Relevant Equations

None

Is my work correct?
I got confused whether the current Splits or not, but i decided against it.

 

[Baluncore]

Is my work correct?

Yes.

I got confused whether the current Splits or not, but i decided against it.

An unloaded potential divider, divides the voltage.
The same current flows through both series resistors.

For part b, I solved it differently, to get the same answer.
Computed current; i = (5V - 3V ) / 5k ;
Then R = 3V / i ;

 

[Edy56]

Yes.An unloaded potential divider, divides the voltage.
The same current flows through both series resistors.

For part b, I solved it differently, to get the same answer.
Computed current; i = (5V - 3V ) / 5k ;
Then R = 3V / i ;

Thank you