Find Range of R4 & U4 for I in [-3A,-1A]

[gruba]

Homework Statement

Find range of resistance R4 and voltage U4 so that the range of current I is $$I \in [-3A,-1A]$$
E=5V,
E4=6V,
Ig=1A,
Ig4= -3A,
R1=2ohm,
R2=3ohm,
R3=5ohm

Homework Equations

-Kirhoff's law
-Potential of nodes method

The Attempt at a Solution

Firstly, I set current I= -3A. Setting potential V3=0 V, current I23=0.25 A.

Using Kirchhoff's law on node 2 ,I12=1.25 A. On node 1 ,I14=1.75 V.

Now potential of nodes are V1=5 V, V2=1.25 V, V3=0 V V4=1.5 V.

With potential of nodes method on node 4, R4=2.09 ohm. Then, U4= -4.5 V.

In my book's solution, it says that R4 starts from 0.22 ohm and U4 starts from -4.5 V.

Could someone check this?

 

[nilesh_pat]

I don't understand why R4 starts from 0.22 ohm and U4 starts from -4.5 V. Can someone explain this? Thank you in advance