Need help answering questions (Voltage source and 3 Resistors)

[Purpleshinyrock]

Homework Statement

1-What is Voltage in R1 when current in R is maximum?

2-Is it possible to make voltage in R1 equal to vab through changing the value of R?

Relevant Equations

V=IR

Hello. I need help arriving to the answers to the following question above.
You will find the circuit attached
for Number 1 I though that crrent would be maximum when resistance is replaced with a wire but I couldn't get a an expression for ut.
as for question number 2 I tried applying node voltage to see If there's an equation to change the value of R so that what is desired happens but had no good results.
Can you help me?
YOUR TIME AND ATTENTION ARE DEEPLY APPRECIATED .
Thank You.

 

[berkeman]

Homework Statement:: 1-What is Voltage in R1 when current in R is maximum?

2-Is it possible to make voltage in R1 equal to vab through changing the value of R?
Relevant Equations:: V=IR

couldnt get a an expression for ut.

What is "ut"?

2-Is it possible to make voltage in R1 equal to vab through changing the value of R?
Relevant Equations:: V=IR

for question number 2 I tried applying node voltage to see If there's an equation to change the value of R so that what is desired happens but had no good results.

If V(R1) = V(AB), then you just have a 2:1 voltage divider overall, right? What has to happen to give you that voltage divider ratio?

 

[Purpleshinyrock]

What is "ut"?If V(R1) = V(AB), then you just have a 2:1 voltage divider overall, right? What has to happen to give you that voltage divider ratio?

Thank you for the reply. The only thing that stayed with me about voltage divider is the formula. Are You saying to apply it to V(r1) and make a relation to Vab and Vr1?
I meant ''Ir'' not ''ut'' it was a misstype appologies.