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.

 

[rezeew]

I understand your frustration and desire to solve this problem. However, without more context and information about the network, it is difficult for me to provide a specific solution. In order to find the total resistance in a network, we need to use Ohm's Law (V=IR) and Kirchhoff's Laws (KCL and KVL) to analyze the circuit and determine the equivalent resistance. It is important to also consider the type of network (series, parallel, or combination) and the values of the resistors in order to determine the most effective method for solving the problem. I suggest reviewing these concepts and carefully examining the given network to see if there are any patterns or simplifications that can be made to make the problem more manageable. Additionally, seeking help from a classmate, teacher, or online resources may also be helpful in finding a solution. Keep in mind that problem-solving in science often requires persistence and creativity, so don't give up and keep experimenting with different approaches until you find the answer.