Physics - transformer / resistance question

In summary, the task was to find the source resistance in a transformer circuit with known values for load resistance, turns ratio, and rms source voltage. The solution involved finding the current through each loop and using Kirchoff's loop rule to find the potential difference across the source resistance. However, the given answer of 194 Ohms does not match the calculated answer. It is possible that there is an error in the problem or the given answer. Further clarification from the professor may be needed.
  • #1
deedsy
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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?
 

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  • #2
Perhaps mutual inductance needs to be accounted for?
 
  • #3
Any help would be great, can't seem to get the answer even if I apply induced emf
 
  • #4
Hello deedsy,

Welcome to Physics Forums!

deedsy said:

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. :smile:

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. :approve:

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.
 
Last edited:
  • #5
collinsmark said:
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.
 

1. What is a transformer in physics?

In physics, a transformer is a device that is used to increase or decrease the voltage of an alternating current (AC). It consists of two or more coils of wire, known as the primary and secondary coils, which are connected by a magnetic core. The transformer works on the principle of electromagnetic induction to transfer electrical energy from one circuit to another.

2. How does a transformer work?

A transformer works by passing an alternating current through the primary coil, which creates a changing magnetic field around the core. This changing magnetic field induces an electric current in the secondary coil, resulting in a transfer of electrical energy. The ratio of the number of turns in the primary and secondary coils determines the voltage transformation of the transformer.

3. What is the difference between step-up and step-down transformers?

A step-up transformer is one that increases the voltage of an AC current, while a step-down transformer decreases the voltage. This is achieved by having a higher or lower number of turns in the secondary coil compared to the primary coil. Step-up transformers are used to transmit electricity over long distances, while step-down transformers are used to lower the voltage for household or industrial use.

4. What is resistance in physics?

In physics, resistance is a measure of how much an object or material opposes the flow of electrical current. It is represented by the symbol R and is measured in ohms (Ω). Resistance depends on factors such as the material, length, and cross-sectional area of the object in question. It is an important concept in understanding the behavior of electricity and is used in various electrical devices and circuits.

5. How does resistance affect a transformer?

In a transformer, resistance can result in energy losses in the form of heat. This resistance is due to the inherent resistance of the wire used to make the coils, as well as any external factors that may increase resistance in the circuit. As resistance increases, the efficiency of the transformer decreases, and more energy is lost in the form of heat. Therefore, transformers are designed to have low resistance in order to minimize energy losses and improve efficiency.

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