Physics - transformer / resistance question

[deedsy]

Homework Statement

In the transformer shown in the figure below, the load resistance RL is 46.0 Ω. The turns ratio N1/N2 is 2.65, and the rms source voltage is ΔVS = 85.0 V. If a voltmeter across the load resistance measures an rms voltage of 27.5 V, what is the source resistance Rs?

I've attached an image of the circuit diagram.

The answer is 194 Ohms

Homework Equations

Vprimary/Vsecondary = Isecondary/Iprimary = Nprimary/Nsecondary

ΔV=IR

The Attempt at a Solution

I've found the current through each loop.
Loop 2: VL/RL = 27.5/46 = .5978 Amps
Loop 1: I2/I1 = N1/N2.... so, .5978/2.65 = .2256 Amps

Here is where I have problems. Can I apply Kirchoff's loop rule to loop 1 (V - Vresistor (=IR) - Vinductor = 0)? And if so, how do I go about finding the potential difference over the large inductor?

 

[deedsy]

Perhaps mutual inductance needs to be accounted for?

 

[deedsy]

Any help would be great, can't seem to get the answer even if I apply induced emf

 

[collinsmark]

Hello deedsy,

Welcome to Physics Forums!

Homework Statement

In the transformer shown in the figure below, the load resistance RL is 46.0 Ω. The turns ratio N1/N2 is 2.65, and the rms source voltage is ΔVS = 85.0 V. If a voltmeter across the load resistance measures an rms voltage of 27.5 V, what is the source resistance Rs?

I've attached an image of the circuit diagram.

The answer is 194 Ohms

Homework Equations

Vprimary/Vsecondary = Isecondary/Iprimary = Nprimary/Nsecondary

ΔV=IR

The Attempt at a Solution

I've found the current through each loop.
Loop 2: VL/RL = 27.5/46 = .5978 Amps
Loop 1: I2/I1 = N1/N2.... so, .5978/2.65 = .2256 Amps

Assuming an ideal transformer (which I'm guessing we are supposed to assume), you currents look correct to me.

Here is where I have problems. Can I apply Kirchoff's loop rule to loop 1 (V - Vresistor (=IR) - Vinductor = 0)?

Yes, you should be able to do that.

And if so, how do I go about finding the potential difference over the large inductor?

Well, you know the potential difference on the smaller (N2) inductor. Can you use that and the transformer's turn ratio to find the potential difference on the primary (larger) inductor?

But before going too far with that, check to make sure the problem statement was copied correctly, including all of the values and what gets measured where. Check that the 194 Ohm answer was copied over correctly. I'm getting a different final answer.

Either I'm doing something wrong myself, or something is wrong with the problem and given answer.

 

[deedsy]

Well, you know the potential difference on the smaller (N2) inductor. Can you use that and the transformer's turn ratio to find the potential difference on the primary (larger) inductor?

But before going too far with that, check to make sure the problem statement was copied correctly, including all of the values and what gets measured where. Check that the 194 Ohm answer was copied over correctly. I'm getting a different final answer.

Either I'm doing something wrong myself, or something is wrong with the problem and given answer.

Hello, thank you for helping. Yes, I found the potential difference for loop one's inductor using the ratios, and then Kirchoff's loop rule to find ΔV across the source resistance. Finally I used Ohm's law to find the source resistance, but like you, am not getting the correct answer.

Unfortunately, all the numbers are copied correctly; I have been struggling with this problem (and variations of it) for awhile now. It seems others are having the same trouble, so I am wondering if the program is having issues. I will talk to my professor about it Monday. I can't think of any other variables I could be overlooking.