Power of Transformer: Primary & Secondary Light Bulb

[steve oliver]

when i compare the brightness of the light bulb in the primary transformer and the secondary transformer (step up transformer) the secondary light bulb is brighter . teacher say because of v^2/r after step up the v increase and so the power. however if i use i^2r after step up i decrease power should be decreased also. whu would i get a different result in different calculating methods

 

[CWatters]

however if i use i^2r after step up i decrease power

How are you measuring or calculating i?

 

[anorlunda]

I don't blame you for being confused. Your transformer raises the voltage and decreases the current, relative to what? Relative to the primary side voltage and current. But what happens on the secondary side also affects the primary side. Considering the two sides independently causes the confusion.

Look up transformers on Wikipedia. https://en.m.wikipedia.org/wiki/Transformer. In the ideal tranfpsformer equations , you can see that you can replace the transformer and the load resistance R, by a single resistance Rp=a*a*Rs, where a is the number of primary side turns divided by the number of secondary side turns, Rs is the load resistance of the light bulb. Rp is the apparent resistance of the light seen from the primary side.

Now you can analyze your circuit using V=I*Rp as if the transformer was not there. If you do that, then the seeming cotraditictions and confusion should go away.

If that is not clear, I can try to draw the pictures for you, when I get access to a real computer.

 

[CWatters]

The point is that the current through the load does not decrease in this situation. The transformer increases the voltage and the load determines the current according to I = V/R. V has been increased (relative to what it was when the load was connected to the primary) so I increases. Hence my question..

How are you measuring or calculating i?

 

[steve oliver]

i get it now thank you

 

[steve oliver]

Then in the following question how should i calculate.
Two identical light bubls x and y are connected respectively to the primary and secondary coils of an ideal step downtransformer.The turn ratio of the transformer is 2:1.Calculate the power dissipated in x and y.
method 1: i^2r x:y=1:4
method 2: v^2/r x:y=4:1
method 3 :vi x:y=1:1
why would be 3 different result?also shouldn't the power in primary =power in secondary?

 

[CWatters]

You made mistakes somewhere...

method 1: i^2r x:y=1:4

i_x = V/R
i_y = 0.5V/R

So using W = i²R you get

W_x = (V/R)² R = V²/R and
W_y = (0.5V/R)² R = 0.25V²/R
Ratio is 4:1

method 2: v^2/r x:y=4:1

V_x = V
V_y = V/2

Using V²/R ...

W_x = V²/R
W_y = (V/2)²/R = 0.25V²/R
Ratio is 4:1

method 3 :vi x:y=1:1

V_x = V
V_y = 0.5V

I_x = V/R
I_y = 0.5V/R

Using W = IV

W_x = V * V/R = V²/R
W_y = 0.5V * 0.5V = 0.25V²
Ratio = 4:1

So they are all the same ratio 4:1

 

[CWatters]

also shouldn't the power in primary =power in secondary?

You are confusing two different things..

a) Power in vs Power out of the transformer - yes it's the same
with
b) Power dissipated in the bulb when connected to the primary vs Power dissipated in the bulb when connected to the secondary - no it's not the same because the bulb draws more power when connected to the primary.

 

[steve oliver]

But shouldn't iy have double current that of ix?

 

[CWatters]

x and y are not the same circuit so Ix and Iy are not related by the transformer equation...

Circuit "x" has the bulb connected to the primary. In that situation there is nothing connected to the secondary of the transformer so the secondary current is zero. Therefore the current in the primary is also zero. The current in the bulb is V/R.

Circuit "y" has the bulb connected to the secondary. The current in the secondary is 0.5V/R (It's 0.5V because it's a 2:1 step down transformer). The current in the primary is equal to half the secondary current or (0.5V/R) / 2.

 

[CWatters]

I will try and do a drawing later. Have to go out for a few hours.

 

[CWatters]

 

[steve oliver]

then what if the light bulb in primary coil is connected with the light bulb in secondary coil. i mean they are in the same circuit.

 

[CWatters]

Then the current drawn from the source V is just the sum of the two (kirchhoff's current law).

Itotal = Ix + Iin = (V/R) + (0.25V/R) = 1.25V/R

Everything else is the same.