Transformer (Power For Load)

[dwn]

Homework Statement

Please see the image attached. We are asked to find the average power (P) delivered to Z_L.

2. Relevant Questions

(My observation of the circuit) The circuit on the left is as follows: V + I1*(5 + jwL) = 0.
For the circuit on the right: V = I2*(Z + jωL)

Is a= N1/N2 or N2/N1?

The Attempt at a Solution

(a) Given that there is no source in the left circuit, we use the RE values from the right circuit:

[B]I[/B][SUB]2(max)[/SUB] = 2A    [B]I[/B][SUB]2(rms)[/SUB] = 2/2 = 1A       [B]P[/B] = 1[SUP]2[/SUP] *60 = 60 W

(b) Since we are given a V_1(rms)= 100∠60° V we can calculate V² by ( a = V₁/V₂ ).

a = N1/N2 = 0.5       V[SUB]2[/SUB]= 100/0.5 = 200V[SUB](rms)[/SUB] 
[B]P[/B] = V[SUP]2[/SUP]/Z    →   200[SUP]2[/SUP]/60 = 666.67 W

(c)

V[SUB]S(max)[/SUB] = 120∠0°   By finding V[SUB]1[/SUB], we are able to find V[SUB]2[/SUB].    V[SUB]S[/SUB]= I[SUB]1[/SUB]*5 + jωL

I thought this was the correct way of solving this since, jωL = V/I but we are not given the frequency ω. So obviously this is not the correct approach.

Can someone please critique and advise on everything. I do have a couple other questions regarding this circuit, but I will wait until the problem is completed. Thank you very much any help!

 

[rude man]

(a) Given that there is no source in the left circuit, we use the RE values from the right circuit:

[B]I[/B][SUB]2(max)[/SUB] = 2A    [B]I[/B][SUB]2(rms)[/SUB] = 2/2 = 1A       [B]P[/B] = 1[SUP]2[/SUP] *60 = 60 W

OK

(b) Since we are given a V_1(rms)= 100∠60° V we can calculate V² by ( a = V₁/V₂ ).

a = N1/N2 = 0.5       V[SUB]2[/SUB]= 100/0.5 = 200V[SUB](rms)[/SUB] 
[B]P[/B] = V[SUP]2[/SUP]/Z    →   200[SUP]2[/SUP]/60 = 666.67 W

No. Your V is right but your Z is not. Use the correct |Z| to get the current, then do I^2 R where R = 60 ohms.

(c)

What is the impedance of the load Z looking at the transformer input? Call that Z'. You have an ideal transformer. What is Z' as a function of Z and a? BTW a = N2/N1 = 2.

Then you can put R=5 ohms in series with the transformer input to compute I1, and you know I2/I1 = N1/N2. Then use |I2| to compute load power as in (b).

EDIT:
It may be simpler to write KVL for the inut and output circuits, realizing V2 = aV1 and I2=I1/a. So you get 2 equations in 2 unknowns: in I2 and V2. Then again P = |I2|^2 R, R = 60.

 

[dwn]

Part B:

Z[SUB]L[/SUB]= 60+j80        I[SUB]2[/SUB]= 200/(60+j80)  = 1.2 - j1.6   
Magnitude of I[SUB]2[/SUB]= 2A
P = 2[SUP]2[/SUP]*60 = 240 W

Part C:

a[SUP]2[/SUP]= Z[SUB]s[/SUB]/Z[SUB]p[/SUB]   Z[SUB]p[/SUB] = 15+j20

I[SUB]1[/SUB]= 120/(20+j20) = 3+j3       Magnitude of I[SUB]1[/SUB] = 4.24A 
I[SUB]2[/SUB]/I[SUB]1[/SUB] = a        2(4.24) = 8.48A = I[SUB]2[/SUB]
[B]P[/B]=8.48[SUP]2[/SUP]*60 = 4314.62W

How does it look now?

Thank you a lot for the guidance. I forgot about the Z_p : Z_s relationship.

 

[rude man]

Getting there.

For (c) you first need to reduce the 120V by sqrt(2).
That reduces your |I1|.
Then, it's a = I1/I2, not the other way around. Remember, a = N2/N1 = 2 here.
That reduces |I2| by a lot.
Then P = |I2|^2 * 60.

 

[rezeew]

I would first like to commend you on your thorough attempt at solving this problem and your willingness to seek advice and clarification. It is important to always question and seek understanding in scientific problems.

In response to your questions, I would like to provide some guidance and corrections:

1. In the relevant questions, the circuit on the left is missing a source, which is necessary to accurately solve for the power delivered to ZL. Without a source, the left circuit is not complete and we cannot accurately determine the current and power.

2. In your attempt at a solution, for part (a), you correctly use the RE values from the right circuit to determine the power delivered to ZL. However, for part (b), the value of a should be N2/N1, not N1/N2. This is because the voltage ratio is V1/V2, not V2/V1.

3. In part (c), you correctly identify that we need to find V2 in order to determine the power delivered to ZL, but your approach to solving for V2 is not correct. To solve for V2, we can use the voltage division formula: V2 = VS*(Z/(5 + jωL + Z)). This will give us the voltage across ZL, which we can then use to calculate the power delivered to ZL.

I hope this helps clarify some of the concepts and correct any mistakes. Keep up the good work and always remember to question and seek understanding in scientific problems.