(adsbygoogle = window.adsbygoogle || []).push({}); 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!

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# Homework Help: KCL with phasors: how to proceed knowing effective values

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