Step up transformer + ac generator question

[tobz102]

Homework Statement

An AC generator, originally designed to provide a peak output of +/- 155V at frequency 60Hz, is required to provide a peak output of +/- 340V at 50Hz. If the generator is connected to a transformer with 200 loops in its primary coil, how many loops should there be in the secondary coil in order to required the output?

Homework Equations

transformer equation? EMF on secondary / EMF on primary = No. coils on secondary / No. coils on primary

The Attempt at a Solution

I don't understand where to start on this? I know that I need to use the above equation but unsure how to get there

 

[rock.freak667]

Break it down to what is happening at the primary (input) and secondary (output)

Primary

Voltage =?
No. of coils = ?

Secondary

Voltage =?
No. of coils = ?

 

[tobz102]

Break it down to what is happening at the primary (input) and secondary (output)

Primary

Voltage =?
No. of coils = ?

Secondary

Voltage =?
No. of coils = ?

I was thinking along the lines of:

Primary V=155V
Coils = 200 loops

Secondary V=340V
Coils=?

But surely this is too much of a simple method and also it gets me the frequency of the a.c current...

 

[rock.freak667]

I was thinking along the lines of:

Primary V=155V
Coils = 200 loops

Secondary V=340V
Coils=?

But surely this is too much of a simple method and also it gets me the frequency of the a.c current...

Well using the transformer equation that is how it should be done.

 

[rwisz]

.

I would approach this problem by first understanding the basic principles behind transformers and AC generators. A transformer is an electrical device that can increase or decrease the voltage of an alternating current (AC) by using two coils, a primary and a secondary, that are connected by a magnetic core. An AC generator, on the other hand, is a device that converts mechanical energy into electrical energy by rotating a coil in a magnetic field.

In this scenario, the AC generator is designed to provide a peak output of +/- 155V at a frequency of 60Hz. This means that the voltage of the AC output fluctuates between +155V and -155V, with a frequency of 60 cycles per second. However, the requirement is to increase the peak output to +/- 340V at a frequency of 50Hz. This means that the voltage of the AC output will now fluctuate between +340V and -340V, with a frequency of 50 cycles per second.

To achieve this, we can use a step-up transformer, which will increase the voltage of the AC output. The transformer equation, as mentioned in the problem statement, is EMF on secondary / EMF on primary = No. coils on secondary / No. coils on primary. This equation tells us that the ratio of the number of coils in the secondary (Ns) to the number of coils in the primary (Np) is equal to the ratio of the EMF (electromotive force) on the secondary (Vs) to the EMF on the primary (Vp).

In this problem, we know the voltage and frequency of the AC output from the generator, and we need to determine the number of coils in the secondary to achieve the desired output. We can rearrange the transformer equation to solve for Ns:

Ns = (Vs/Vp) * Np

Substituting the known values, we get:

Ns = (340V/155V) * 200 = 436.77

Therefore, the secondary coil should have approximately 437 loops to achieve the required output of +/- 340V at 50Hz. However, it is important to note that this is an ideal calculation and does not take into account losses in the transformer and generator. In reality, the number of coils in the secondary may need to be slightly higher to compensate for these losses.

In conclusion, by understanding the principles of transformers and AC generators, and using the transformer equation