Calculate RMS Voltage for 120V, 60Hz Transformer

[debwaldy]

Homework Statement

Hi, so I am just starting an rms voltage question but I'm a small bit confused.
The problem states: A transformer having 90 turns on the primary and 2250 turns on the secondary is connected to a 120V, 60Hz source. Calculate a) the rms voltage and b) the peak voltage at the secondary.

Homework Equations

Vrms = Vm/2^0.5

Ns/Np = Vs/Vp

The Attempt at a Solution

So far i have said:
Vs = (120)(2250)/(90) from the second equation above
=> Vs = 3000V

After this i was going to say that the rms voltage is Vs/2^0.5
however i have been given the answer and it says that the rms voltage is simply 3000V. I don't understand this and would appreciate any explanation anyone could offer?
I realize i also haven't used the 60Hz value,so i may be missing an equation??
Thanks for any help
debs

 

[marcusl]

Your Vs is the secondary rms voltage because it was calculated from an rms primary value. So far so good. The frequency is unimportant except to indicate that you are working with AC (alternating current), which means a sinusoidal waveform. To finish the problem and calculate the peak voltage, what do you know about the relation between peak and rms amplitudes for a sine wave?

 

[ogb p]

Hi Debs,

To calculate the rms voltage for a transformer, you will need to use the following equation:

Vrms = Vp * (Ns/Np)

Where:
Vp = peak voltage at the primary side
Ns = number of turns on the secondary side
Np = number of turns on the primary side

In this case, Vp = 120V, Ns = 2250, and Np = 90. So, plugging in these values, we get:

Vrms = (120V) * (2250/90)
= 3000V

So, the given answer of 3000V is correct. The 60Hz value is not needed in this calculation as it is used to determine the frequency of the voltage, not the magnitude.

Hope this helps clarify the solution for you. Keep up the good work!