Finding Vx, Is, and Power in a Dependent Source

[sevag00]

Homework Statement

Find V_x, I_s and power on the dependent source.

The Attempt at a Solution

http://s17.postimg.org/3x4hszzkf/002.jpg

 

[gneill]

Your determination of v_x is fine. However, I_s is not the only current flowing through the 4 Ω resistor; there's some current coming from the 29 A source, flowing through the 4 Ω + I_s combination, then to the components on the right.

You should be in a position to know how much current is entering and leaving that middle bit.

 

[sevag00]

I did KCL on node a and got 30 A. Also calculated the current through the 4 Ω resistor -1.5 A.
Then KCL on node b, I_s = 31.5 A

 

[gneill]

Draw the directions of the currents through the resistors. Then do KCL again

 

[sevag00]

Oh ok. 28 not 30. Then I_s = 26.5.

 

[gneill]

Which resistors?

All of them. You have the voltages across them all.

 

[sevag00]

Oh ok. 28 not 30. Then I_s = 26.5.

...

 

[gneill]

No, not 26.5 A. I think you've got a current direction wrong. Sketch them on your diagram and pay attention to polarities -- remember, Vx is negative...

 

[sevag00]

Here's the new sketch. If I'm not wrong then 29.5 A.

 

[gneill]

Here's the new sketch. If I'm not wrong then 29.5 A.

You're not wrong

 

[sevag00]

 

[sevag00]

Another day, Another KVL-KCL problem.

Find V₀ using KVL-KCL and Ohm's law.

Here's my solution
http://s21.postimg.org/usa92r31z/001.jpg

 

[gneill]

You really should place new questions in new threads, if for no other reason than more people are likely to see it.

For this problem it looks like you've got the right ideas, but you're losing way too much accuracy by not keeping enough decimal places in your intermediate results. Keep intermediate values in fraction form or keep several more decimal places ("guard digits").

For example, knowing that I1 is 4 mA and it's flowing through a 4 kΩ resistor you can tell that the potential drop across that resistor should be 16 V exactly. That means the sum of the 42V supply and the drop across the 6 kΩ resistor must add to 16V, so that the drop is 26 V across that resistor. But in your determination of i2 you rounded the result to 4.3 mA, and then when you calculated the potential drop across that resistor you arrived at 25.8 V.

The situation gets worse when you round small values, as the resulting percentage change is more drastic. You determined the current through the 18 kΩ resistor to be 1.63 mA, but it should have ended up as 1.889 mA. So the early roundings of values has landed you with a 14% error so far...

 

[sevag00]

Is it enough if i write three decimal digits?

 

[gneill]

Is it enough if i write three decimal digits?

Three is better, yes. If your calculator has enough memory locations, write three digits but use the stored full-accuracy values for calculations. As always, round final results to the appropriate number of significant figures.