What Is the Correct Current Equation to Induce Given Flux in a Circuit?

  • Thread starter Sarah0001
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In summary: I would be happy to look for an equation that relates the flux through a wire loop versus the current flowing through the loop.
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Sarah0001
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1. Problem Statement:
flux in a flux circuit varies according to the equation Φ = sin ωt.
Using a constant k, what is the equation for a current which could induce the flux in the flux circuit above?


Homework Equations


Φ = sin ωt.

The answer given is :
e12ee062d538a768a369f9e7806a3248f1c870b0


The Attempt at a Solution


My attempt at this solution is, that Current that induces the flux (regardless of whether the flux varies or not due to current) and is directly proportional to the flux as a result . Flux and current are in phase is my understanding (correct me if I'm wrong).

Thus. I = Ksinwt
however the answer gives -Ksinwt, I am confused on how they get the -ve

I know Emf induced and thus the current induced are proportional to the (-ve) rate of change of flux linkage,

however the question asks for a current which would induce the flux, not the other way round (where only a change of flux could only induce current) ,

hence it would be solely a proportional relationship between current and flux (flux dependent on current),
so surely the answer is Ksinwt as nothing is being opposed - I am unsure what the negative is indicating here about the current if the answer given is correct.
 
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Look for an equation that relates the flux through a wire loop versus the current flowing through the loop. If you drive a sinusoidal current through a wire loop, what is the equation for the flux as a function of time through the loop's area? :smile:
 
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berkeman said:
Look for an equation that relates the flux through a wire loop versus the current flowing through the loop. If you drive a sinusoidal current through a wire loop, what is the equation for the flux as a function of time through the loop's area? :smile:
Hi, thank you for your response. I am unsure what what equation that would be and how it helps to solve the question.
 

FAQ: What Is the Correct Current Equation to Induce Given Flux in a Circuit?

What is a transformer and how does it work?

A transformer is an electrical device that is used to transfer electrical energy from one circuit to another through electromagnetic induction. It consists of two or more coils of wire called windings, which are connected by a magnetic core. When an alternating current flows through the primary winding, it creates a changing magnetic field, which induces a voltage in the secondary winding. This allows for the transfer of energy between the two circuits without a direct electrical connection.

What is the purpose of a transformer in an electrical circuit?

The main purpose of a transformer is to change the voltage level of an alternating current. It can step up or step down the voltage depending on the ratio of the number of turns in the primary and secondary windings. This is useful for transmitting electricity over long distances, as higher voltages are more efficient for long-distance transmission. Transformers are also used to isolate circuits, match impedance, and provide galvanic isolation for safety purposes.

What is flux and how does it relate to transformers?

Flux is a measure of the strength of a magnetic field. In a transformer, the changing magnetic field created by the alternating current in the primary winding induces a voltage in the secondary winding. This is due to the principle of electromagnetic induction, which states that a changing magnetic field will induce a voltage in a nearby conductor. The amount of flux in a transformer is dependent on the number of turns in the windings, the strength of the magnetic field, and the permeability of the core material.

What are the different types of transformers?

There are two main types of transformers: step-up transformers and step-down transformers. Step-up transformers have a higher number of turns in the secondary winding, resulting in an increased output voltage compared to the input voltage. Step-down transformers have a lower number of turns in the secondary winding, resulting in a decreased output voltage. Other types of transformers include autotransformers, which have a single winding that acts as both the primary and secondary winding, and isolation transformers, which are used for safety purposes to isolate circuits.

How do you calculate the efficiency of a transformer?

The efficiency of a transformer is the ratio of output power to input power, expressed as a percentage. It can be calculated by dividing the output power by the input power and multiplying by 100. In an ideal transformer, where there is no energy loss, the efficiency would be 100%. However, in real transformers, there is always some energy loss due to factors such as resistance in the windings, hysteresis, and eddy currents. Therefore, the efficiency of a transformer is typically between 90-99%.

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