I need help with the following problem:
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
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?
Best Answer
By applying the superposition theorem to your circuit I have noticed that the current you are looking for can only be dependent from voltage source E, because when you are looking at another source, E is shorted, so your current gets 0A. So now it depends on E alone (all other sources shorted or open).
So R1 gets in serial to R4 and R2 and R3 get just serial, too. Finally the serial resistance groups are in parallel.
As R4 is effectively rising with I, it must be that R4∈[0.1 Ω; 11.3 Ω].
Hope this helped a bit, though late....