# KCL with phasors: how to proceed knowing effective values

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1. Nov 28, 2017

### Granger

1. The problem statement, all variables and given/known data
I have the following problem. Consider a circuit node where 3 sinusoidal currents with the same frequency converge, i1 i2 and i3. Knowing that the effective values of i1 and i2 are I1ef=1A and I2ef=2A. What can we say about I3ef:

Options:
$$(a)1A \leq I_{3ef} \leq 3A$$
$$(b)0 \leq I_{3ef} \leq 3A$$
$$(c)2A \leq I_{3ef} \leq 3A$$

2. Relevant equations
3. The attempt at a solution

My attempt:
So using KCL we have:
$$i_1+i_2+i_3=0$$

Using phasors
$$\overline{I_1}+\overline{I_2}+\overline{I_3}=0$$

where $$\overline{I_i}=I_ie^{j\phi_i}$$

Then
$$I_1e^{j\phi_1}+I_2e^{j\phi_2}+I_3e^{j\phi_3}=0$$

Because $$I_i=I_{efi}\sqrt{2}$$ then:

$$I_{ef1}\sqrt{2}e^{j\phi_1}+I_{ef2}\sqrt{2}e^{j\phi_2}+I_{ef3}\sqrt{2}e^{j\phi_3}=0$$

Now I'm stuck in this. I don't know how should I proceed from this to obtain the interval of values for I3ef. I think the complex exponentials are what is bothering me. Can someone help me?

Thanks!

2. Nov 28, 2017

### cnh1995

I believe you don't need complex exponentials here. Just think about the case where you'll get maximum and minimum values for i3.
What should be the phase differene between any two currents in that case?