Principle of Superposition in Circuits

[zealeth]

Homework Statement

Assume that V = 4.8V and I = 3.2mA. Find Ix in the figure using the principle of superposition.

Homework Equations

V=IR
Kirchhoff's Current Law
Kirchhoff's Voltage Law
Total response = ∑responses from each individual source

The Attempt at a Solution

I believe I'm having trouble in simply solving for I_x in each circuit, but if you see any other mistakes please let me know.

Replacing the voltage source with a short circuit, we have:

Not really sure how to go about solving this one. If I had to guess, I would right a KCL at the bottom node such that:

I + the current across the 2k and 1k Ohm resistors = I_x

Replacing the current source with an open circuit, we have:

Summing the resistances now in series and solving for i_total:

4k * i_total = 4.8

i_total = .0012 A

If I'm not mistaken, this should be equal to I_x_2.

I_x = I_x_1 + I_x_2 = ?

 

[FOIWATER]

Are you familiar with the current divider rule? It is helpful in solving the first circuit.

Rather than just looking up current divider, try to prove it using the result

 

[FOIWATER]

Let me help by proving the current divider rule for your circuit, then you can proceed to finish your superposition.

The way your circuit is set up (the first one), you have a current source feeding current into two branches right. OK, those branches are in parallel. The voltage across them is equal so we can write the equations:

1K(I1) = 3K(I2)

You can realize that I2 is just I total minus I1. You know I total and the resistances so from here you have Ix1

Does this make sense?

 

[zealeth]

I am familiar with the current divider rule and attempted to use it earlier (forgot to mention in post) , but it gave me the wrong answer so I did not think that was how to solve it. The mistake I made was using 0.0032 as a positive number, which gave me the incorrect result. Looking at your post proving the current divider, I was able to correct my mistake and solve the problem. Thanks.

 

[FOIWATER]

Happy to hear that.

You're welcome