Homework help: Transformer Current

[Aryan Andaleeb]

Homework Statement

If we denote:

Alternating current in the primary coil as I₁
Alternating current in the secondary coil as I₂

Similarly, we denote,

Number of turns in primary coil as N₁
Number of turns in secondary coil as N₂

And, we denote,

Voltage generated across primary coil as V₁
Induced voltage across secondary coil as V₂

Okay, now let the load, R, be connected to the secondary.

Now, exactly on which factors do the value of I₂ depend on?

Homework Equations

Here,

V₁ / V₂ = N₁ / N₂ = I₂ / I₁ -------i

Again,

I₂ = V₂ / R ------------------------ii

Besides,

I₁ = V₁ × Z --------------------iii
[Where, Z means electrical imppedance in the primary coil, generated by the ac generator]

The Attempt at a Solution

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But,

I₂ = I₁ × V₁ / V₂ ----------------- iv

and also,

I₂ = I₁ × N₁ / N₂ -----------------v

Where, each of the magnitude on the right-hand side of both the equation is constant.

So, is the value of I₂ dependent upon R ?


If the answer is yes, then,

as R is variable, so,(according to equation no.ii) I₂ is variable.

Therefore, (according to equation no.iv and v) I₁ is variable.

But, according to equation no. iii

I₁ = V₁ × Z

Now, I'm getting a bit confused. How can this equation (equation no.iii) be true?

Since,

I₁ is variable depending on R

But, at the same timeV₁ is constant.

Z is constant.So, its getting difficult to predict the controlling factors of I₂

Please help. I've stuck in this problem for a few days!

 

[berkeman]

Welcome to the PF.

The source voltage V1(t) is transformed to the secondary voltage V2(t) by the turns ratio. The secondary current is determined by the secondary voltage and the load resistance. For the ideal transformer driven by an ideal voltage source (that has zero internal resistance), that's about all there is to it. Does that help?

 

[Aryan Andaleeb]

The source voltage V1(t) is transformed to the secondary voltage V2(t) by the turns ratio. The secondary current is determined by the secondary voltage and the load resistance. For the ideal transformer driven by an ideal voltage source (that has zero internal resistance), that's about all there is to it. Does that help?

That's alright.

But how is the primary current determined in a transformer?

And thanks a lot for your help.

 

[CWatters]

Typically V₁, R and N₁:N₂ are known. The sequence of working out the other variables is usually as follows...

Secondary voltage is determined by the winding ratio..

V₂ = V₁ * N₂/N₁

Secondary current is determined by the load...

I₂ = V₂/R

Primary current is determined by the winding ratio...

I₁ = I₂ * N₂/N₁

 

[Aryan Andaleeb]

Typically V₁, R and N₁:N₂ are known. The sequence of working out the other variables is usually as follows...

Secondary voltage is determined by the winding ratio.

V₂ = V₁ * N₂/N₁

Secondary current is determined by the load...

I₂ = V₂/R

Primary current is determined by the winding ratio...

I₁ = I₂ * N₂/N₁

Okay, I agree with you.

But, now, isn't this true as well?

I₁ = V₁ × Z


[Where, Z means electrical impedance in the primary coil, generated by the a.c. generator]

 

[cnh1995]

But, now, isn't this true as well?

I1 = V1 × Z

Are you familiar with the concept of magnetizing current? Im=V1/Z will be the magnetizing current which is required to create the necessary magnetic flux in the core. When secondary is open, I2=0. Hence I1=I_m. Now when you connect a load (say R), current I2 will flow in the secondary given as I2=V2/R. This will create its own mmf to demagnetize the primary mmf . Hence, to cancel out this demagnetizing mmf, primary draws a current I1 which is 180^o out of phase with I2. Also, its magnitude is N2/N1 times that of the primary current such that there will mmf balance N1I1=N2I2. Note I1 and I am aren't same. The "net" primary current will be vector sum of I am and I1 (which themselves are 90° apart electrically). Im=I1 when I2=0. In introductory physics course, I am can be neglected since it is really small compared to I1. That's where permeability of the core material comes in picture. I am in case of air core would be 1000 times less than that in case of air core. This is just a brief description. You'll get more from experts here on PF.

 

[CWatters]

But, now, isn't this true as well?

I1 = V1 × Z

[Where, Z means electrical impedance in the primary coil, generated by the a.c. generator]

Yes but Z isn't constant. The current in the secondary causes a flux which opposes the primary flux and effectively reduces the impedance Z.

Edit: Actually I think the equation should be I₁ = V₁/Z
Edit: Cross posted with chn1995

 

[Aryan Andaleeb]

Im in case of air core would be 1000 times less than that in case of air core.

What do you mean here?

 

[cnh1995]

What do you mean here?

Permeability of iron is 1000 times more than that of air. So, magnetizing current required will be 1000 times less i.e. you'll get same magnetic flux with 1000 times smaller current. You'll need to study the magnetic behavior of transformer.