What is the correct equation to solve this power and voltage problem?

[CAT 2]

Homework Statement

A 4.0 Watt toy motor is connected to a secondary circuit of a transformer with 60 loops and a current of 0.10 A. The primary voltage is 120 V

Homework Equations

Vp / Vs = Ip / Is

Ip = Pp / Vp[/B]

The Attempt at a Solution

1. [/B]Vp / Vs = Ip / Is
120 V / 40 V = Ip / 0.10 A
0.3 A = Ip OR

Ip = Pp / Vp
Ip = 4 W / 120 V
Ip = 0.0333 AI have found people using both equations to solve this problem. Which one is correct? Did I just somehow put on the wrong values or something? I thought maybe the first one because in my course the second one was used to deal with circuits, and the first one was commonly used in the above type problems. But the above problem is sort of a circuit. Can anybody help me with this? It would be much appreciated!

 

[kuruman]

The statement of the problem does not specify what one is asked to solve for. Can you post that?

 

[CAT 2]

Sorry,

I am solving for current in the primary coil (Ip). I didn't know which equation was correct, because both could be used and they didn't come up with the same answer. I have already found that Vs = 40 volts.

 

[CAT 2]

Does that help?

 

[kuruman]

Does that help?

Your first solution is incorrect. The power (P = I V) is the same on both sides so you have I_p V_p = I_s V_s.
This gives I_p×120 V = 40 V × 0.1 A → I_p = (4 /120) A = 0.0333 A, the same as the second solution.

 

[CAT 2]

So are you saying I messed up with my numbers? Or the power (P = I V) is the correct solution.

 

[kuruman]

So are you saying I messed up with my numbers?

I am saying you messed up your algebra, not your numbers. Your solution 1 says,

1. Vp / Vs = Ip / Is

Where did you get this? If you cross-multiply, you get I_sV_p = I_pV_s which is incorrect. As I stated in post #5, the correct expression is I_p V_p = I_s V_s.

 

[CAT 2]

This is what my course said, does that change anything?

 

[Merlin3189]

That is not the formula you used.in #1. Look carefully at the last line in your text and compare it with the first line of 3.1 in post #1.

 

[kuruman]

This is what my course said, does that change anything?

It does not change anything. It just confirms that I_p V_p = I_s V_s, what I already had in post #7.

 

[CAT 2]

Thanks for all the help guys, I think I figured it out and 0.33333 is the proper answer. Am I right on this one?

 

[kuruman]

Ip = 0.0333 A

Thanks for all the help guys, I think I figured it out and 0.33333 is the proper answer. Am I right on this one?

Which one is right do you think?

 

[CAT 2]

Woops typo, I meant 0.033333... Is that better?

 

[kuruman]

Woops typo, I meant 0.033333... Is that better?

Yes, much better.

 

[LonelyElectron]

Yes, much better.

I have the same question and no matter how I many times I try I always got 0.3 with the Ip/Is = Vp/Vs, and with the Ip/Vp = Is/Vs... I then did P=VI, which got 0.03 A, but the power I used in the equation was the power given for the primary circuit. Does that mean it won't work with secondary voltage and current, or is the power consistent throughout both circuits? I'm so confused!

 

[kuruman]

I have the same question and no matter how I many times I try I always got 0.3 with the Ip/Is = Vp/Vs, ...

No matter how many times you try with this equation you will get the wrong result because the equation itself is wrong. I have indicated as much in posts #5, #7 and #10.

The correct equation is Ip Vp = Is Vs which gives Ip /Is =Vs/Vp. You have Vp/Vs on the right side.

 

[LonelyElectron]

No matter how many times you try with this equation you will get the wrong result because the equation itself is wrong. I have indicated as much in posts #5, #7 and #10.

The correct equation is Ip Vp = Is Vs which gives Ip /Is =Vs/Vp. You have Vp/Vs on the right side.

Okay, so:
Ip/Is = Vp/Vs
Ip=VpIs/Vs
Ip=(120 V)(0.10 A)/40 V
Ip=0.3

Still getting 0.3... Am i manipulating the equation wrong?

 

[Merlin3189]

I'm afraid you are still getting it wrong. Compare your #17 with Kuruman's #16.

The equation Ip Vp = Is Vs is a statement of the primary power = secondary power. P_P = P_S

The equation with I_P / I_S and V_{P / VS} is about the ratio of current and voltage in the primary and secondary.

But you keep saying they are the same. That is wrong. If the power stays the same, then if the voltage goes down, the current goes up and vice versa.
The ratio of currents is the inverse of the ratio of voltages.

So no t $\frac {I_P} {I_S} = \frac {V_P} {V_S} \ \ but \frac {I_P} {I_S} = \frac {V_S} {V_P}$ The voltage ratio must be upside down (inverse) compared to the current ratio.

Does that help?

 

[kuruman]

Still getting 0.3... Am i manipulating the equation wrong?

No. You just didn't read my post #16 where I indicated that

Ip/Is = Vp/Vs

is wrong, yet you insist on using it. It does not follow from Ip Vp = Is Vs.