Power loss in transmission lines (Electromagnetic Induction and Faraday's Law)

[confusedbyphysics]

Show that the power loss in transmission lines, PL, is given by PL = (PT)^2 X R/(V^2), where PT is the power trasmitted to the user, V is the delivered voltage, and R is the resistance to the power lines.

I don't even know where to start. I am so confused by this chapter, I don't know what this question has to do with magnetic flux and Lenz's law and the other stuff in the chapter. Any help please??

 

[nrqed]

Show that the power loss in transmission lines, PL, is given by PL = (PT)^2 X R/(V^2), where PT is the power trasmitted to the user, V is the delivered voltage, and R is the resistance to the power lines.

I don't even know where to start. I am so confused by this chapter, I don't know what this question has to do with magnetic flux and Lenz's law and the other stuff in the chapter. Any help please??

It has nothing to do with Lenz law or flux, indeed.

Think of a simple circuit with two resistors (representing the resistance of the line and the resistance of the load (where the user is drawing power from).

You have $P_L = R_1 I^2$ and $P_T = R_2 I^2$ where $R_1$ is the resistance of the lines. You also have $V = R_2 I$ where V is the voltage delivered to the user. Use the last two equations to isolate I and plug in the first and you will get the answer. (also, you could use directly $P_T = V I$ which gets you to the answer faster).

Pat

 

[kyle8921]

I can understand your confusion with this topic. However, let me try to explain the relationship between power loss in transmission lines and electromagnetic induction, specifically Faraday's Law.

Faraday's Law states that a changing magnetic field can induce an electric current in a conductor. In the case of transmission lines, the power being transmitted creates a changing magnetic field, which in turn induces an electric current in the power lines.

This induced current in the power lines creates a power loss, as it encounters resistance in the form of the material of the power lines. This resistance is represented by the variable R in the equation provided.

Now, let's look at the other variables in the equation. PT is the power being transmitted to the user, which is the amount of power that is initially generated. V is the delivered voltage, which is the voltage that is delivered to the user's location. This voltage is lower than the initial voltage due to the power loss in the transmission lines.

Bringing all of these variables together, we can see that the power loss in transmission lines, PL, is directly proportional to the square of the power transmitted (PT^2) and inversely proportional to the square of the delivered voltage (V^2). This relationship is consistent with Faraday's Law, as the induced current and resulting power loss increase with the amount of power being transmitted and decrease with the delivered voltage.

I hope this explanation helps to clarify the relationship between power loss in transmission lines and electromagnetic induction. If you have any further questions or concerns, please do not hesitate to reach out.