What is the solution to this transformer problem?

[VitaX]

Homework Statement

[PLAIN]http://img192.imageshack.us/img192/8428/circuits.png

Homework Equations

\frac{V_L}{V_s} = \frac{nR_L}{n^2 R_s + R_L}

R_s = \frac{R_L}{n^2}

P = \frac{V_L^2}{R_L}

The Attempt at a Solution

How should I go about solving this problem? Do I have to convert it to an equivalent circuit? If so how would the end result look exactly? I haven't seen any good examples in the book of creating equivalent circuits of transformers so I'm a little unsure of what to do.

 

[NascentOxygen]

It looks like n₂ is their way of expressing the turns ration of that transformer, 1:n₂. So in place of the transformer with 8k in its secondary, you can show a new resistor R_S in series with your resistor R, that new resistor bring R_L transformed by the square of the turns ratio, as they indicate.

 

[VitaX]

It looks like n₂ is their way of expressing the turns ration of that transformer, 1:n₂. So in place of the transformer with 8k in its secondary, you can show a new resistor R_S in series with your resistor R, that new resistor bring R_L transformed by the square of the turns ratio, as they indicate.

In part a) I found n2 to be 10, but how do I find the max power now? I used the equation I posted in the OP to find the load voltage then used P=\frac{V_L^2}{R_L} but I get 115.2 W as power when the book has 10,000 W roughly. Perhaps it's because I use the wrong value for R_s. I used 20 Ohms. Should it be different? Or it could be because of the n value I use. I put in 10.

 

[NascentOxygen]

In part a) I found n2 to be 10

as do I

but how do I find the max power now?

Are you talking about part (a) or part (b)?

I used the equation I posted in the OP to find the load voltage then used P=\frac{V_L^2}{R_L} but I get 115.2 W as power when the book has 10,000 W roughly.

It can't be thousands of watts. Isn't that a 20 ohm source resistance? So you want the transformed impedances to be of that order, too, so the current from the 120v source is going to be less than 3 amps. (Even were you to short circuit the transformer windings, that 20 ohm will limit the current to 6 amps.)

Perhaps it's because I use the wrong value for R_s. I used 20 Ohms. Should it be different?

I see nothing to indicate a different Rs.

Or it could be because of the n value I use. I put in 10.

In part (b) you are told n1 is 5, and required to find the new n2. So there is no place for using an n of 10.

FWIW, I calculate 1.3125 A is drawn from the 120v supply, in part (b).

 

[VitaX]

as do I

Are you talking about part (a) or part (b)?

It can't be thousands of watts. Isn't that a 20 ohm source resistance? So you want the transformed impedances to be of that order, too, so the current from the 120v source is going to be less than 3 amps. (Even were you to short circuit the transformer windings, that 20 ohm will limit the current to 6 amps.)

I see nothing to indicate a different Rs.

In part (b) you are told n1 is 5, and required to find the new n2. So there is no place for using an n of 10.

FWIW, I calculate 1.3125 A is drawn from the 120v supply, in part (b).

Yeah I was talking about part a) Apparently some others were able to get the 10,000 W power for part a that was int he back of the book though I couldn't really follow what they did.