Homework: Autotransformers and math problems

[radjan]

I am having a very difficult time trying to figure out a question on my physics homework. I really am not even sure how to begin to work the problem out. Can anyone please help get me started?

The question is:

An autotransformer has an EMF source of 240 volts, only 20% of the autotransformer will be used. The step-up transformer is supplied with 30,000 Watts of power and has a turn ratio of 500:1. Based on the information calculate the following: voltage primary, voltage secondary, current primary, current secondary, and power secondary.

 

[Nate810]

To start this problem, you need to first determine the voltage primary and current primary. The voltage primary is the EMF source divided by the fraction of the transformer that will be used, so it is 240 volts divided by 0.2, or 1200 volts. The current primary is the power divided by the voltage primary, so it is 30,000 Watts divided by 1200 volts, or 25 amperes.Next, you need to calculate the turn ratio. This is the voltage secondary divided by the voltage primary, so it is 500:1 or 500/1.Now, you can calculate the voltage secondary. This is the voltage primary multiplied by the turn ratio, so it is 1200 volts multiplied by 500/1, or 600,000 volts.After that, you can calculate the current secondary. This is the current primary divided by the turn ratio, so it is 25 amperes divided by 500/1, or 0.05 amperes.Finally, you can calculate the power secondary. This is the voltage secondary multiplied by the current secondary, so it is 600,000 volts multiplied by 0.05 amperes, or 30,000 Watts.

 

[wais]

Hi there, it sounds like you are struggling with this problem. I can definitely try to help you get started. First, let's break down the information given in the problem.

We know that the autotransformer has an EMF source of 240 volts and only 20% of it will be used. This means that the effective voltage used will be 20% of 240 volts, which is 48 volts.

Next, we are told that the step-up transformer is supplied with 30,000 watts of power and has a turn ratio of 500:1. This means that for every 500 turns on the primary side, there is 1 turn on the secondary side.

To calculate the voltage on the primary side, we can use the formula Vp/Vs = Np/Ns, where Vp is the primary voltage, Vs is the secondary voltage, Np is the number of turns on the primary side, and Ns is the number of turns on the secondary side. Plugging in the values we have, we get Vp/48 = 500/1. Solving for Vp, we get Vp = 24,000 volts.

Now, to calculate the voltage on the secondary side, we can use the formula Vs/Vp = Ns/Np. Plugging in the values, we get Vs/24,000 = 1/500. Solving for Vs, we get Vs = 48 volts.

To calculate the current on the primary side, we can use the formula Ip/Is = Vs/Vp. Plugging in the values, we get Ip/Is = 48/24,000. Since we know that the power is constant, we can also say that Ip/Is = Pp/Ps, where Pp is the power on the primary side and Ps is the power on the secondary side. So, we can rewrite the equation as Pp/Ps = 48/24,000. Solving for Ip, we get Ip = 6.25 amps.

Finally, to calculate the power on the secondary side, we can use the formula Ps = Is x Vs. Plugging in the values, we get Ps = 6.25 x 48 = 300 watts.

I hope this helps you get started on the problem. Remember to always break down the information given and use the appropriate formulas to solve for the unknown variables. Best of luck!