Find total resistance in a network

[STEMucator]

I can't get this last problem in the chapter. I am asked to find $I_x$ in the following network:

My first hunch was to apply KCL to the node above the $2I_x$ source:

$10 + 2I_x - \frac{V}{2} - 3 + I_x + \frac{V}{5} + \frac{V}{10} = 0$

Where I have assumed the voltage $V$ is across all components in parallel. From here I've tried various things, but to no avail.

 

[phinds]

your v/5 term and your v/10 term add up to be Ix, but you've added them in again anyway. Not good.

can you compress the 10ma and 3ma sources down to one source and reduce all the resistors down to one resistor to get an expression for V that is only in terms of Ix and the total resistance?

That's probably too many hints already. You should be able to take it from there.

 

[STEMucator]

your v/5 term and your v/10 term add up to be Ix, but you've added them in again anyway. Not good.

can you compress the 10ma and 3ma sources down to one source and reduce all the resistors down to one resistor to get an expression for V that is only in terms of Ix and the total resistance?

That's probably too many hints already. You should be able to take it from there.

Thank you sir, every problem in chapter 2 is now complete (there was a lot in this chapter, > 100). I obtained $I_x = - 1.5 mA$.

I can finally take it easy after all that, feels like an abyss in my brain right now. I owe you one.

 

[phinds]

Thank you sir, every problem in chapter 2 is now complete (there was a lot in this chapter, > 100). I obtained $I_x = - 1.5 mA$.

I can finally take it easy after all that, feels like an abyss in my brain right now. I owe you one.

Glad to hear it.