Please see attached file.
Assuming that all values are known. Now I need to compute \(i_{1}\)
I can caculate \(i_{1}\) easily by using KVL, KCL laws but I wonder why the method that I did don't work.
In this case, I consider current source ideal and therefore it has infinitive resistance. Hence, the combined resistance of \(R_{2}\) and current source is equal to \(R_{2}\). The combined resistance of the circuit will be \( R{1} + R {2}\) and the current \(i_{1} =\dfrac {V} {R_{1}+R_{2}}\). I know this is wrong but I cann't explain it. Hope anyone could help me out.

 

It is true that the combined resistance of R1 and R2 is R1 + R2.
But the current in R2 is not i1.

By KCL, the current in R2 = i1 + I.

By KVL, V = i1R1 + (i1 + I)R2.

 

It is true that the combined resistance of R1 and R2 is R1 + R2.
But the current in R2 is not i1.

By KCL, the current in R2 = i1 + I.

By KVL, V = i1R1 + (i1 + I)R2.

Thanks, MrChips!
Do you meant that the model of resistor R2 and current source as a resistor is wrong?
If this is correct, then i1 has to equal V/(R1+R2).

 

i1 is not equal to V/(R1 + R2).
This assumes that the voltage across R2 is i1 x R2 which is incorrect.
The voltage across R2 is (i1 + I) x R2.

You must take into account I.

 

It is true that the combined resistance of R1 and R2 is R1 + R2.
But the current in R2 is not i1.

I'm confused by this claim. R1 and R2 are not in series, so what does the combined resistance R1+R2 represent?

I would recommend taking R2 and the current source and converting them into a Thevenin equivalent. Then you have two voltage sources and two resistors all in series and finding the current is trivial (provided care is taken to get the polarities of the sources correct).

 

Sorry. I suspected you would come back and get me for this. I retract my statement.

The op is trying to assume the model of the current source is one with infinite resistance.
He forgot to include the value of I.

The voltage across R2 is (i1 + I)R2.
This is equal to i1 x R2 if I = 0. In which case, R1 and R2 combined is R1+R2 if and only if I = 0.

 

Sorry. I suspected you would come back and get me for this. I retract my statement.

We do tend to keep each other honest, don't we?