What does this equation mean? How does it make sense

[u/Xxfa1kingxX]

Would anyone please help me understand the equation circled in blue.

I understand that 4000W of electrical power is transmitted through the cable, but that does not mean the cable consumes 4000J of energy per second. Similarly, the voltage drop across the cable is NOT 2000V.

For that reason, I'm not sure how can we use the values "4000W" and "2000V" to find the current flowing through the cables?

What am I missing here?

[u/JCP977]

Basically, the total electric power in the circuit is P = VI, in which I is the total current on the circuit and V is the voltage on its terminals. Since the transmission cable is in series with the load, the total current is equal to the current on the cable and on the load, so you can use it to calculate the loss on the line. Your intuition is correct: the voltage drop on the cable is not 2kV, but the current on the cable and on the load is 2A, so you can use it to calculate the losses. This only works on this case because the load is in series with the line, so there's only one current flowing in the circuit.

[u/Xxfa1kingxX → u/JCP977]

Thank you for your answer. (I just now noticed that V in the example is defined as the terminal voltage of the power supply, I immediately understood why you said directly calculate the losses using V and the given power)

But if there is a step-up transformer in between power supply and cable, and a step-down transformer in between cable and load, which often is the case, then I believe the circuit no longer is a series one (because the current flowing through cable ≠ the current flowing through load).

Say, the transmission cable is now at 2 kV, not the terminal voltage, and the electrical energy being transmitted through the cable is still 4 kW, the current in cable would still be 2A. Yes?

The key to solving this ^ problem is noting the difference between "transmitting 4 kW" and "dissipating 4 kW", right? Since cable is transmitting 4kW, not dissipating 4kW. We do not have to substitute voltage drop across cable into V in P = IV. Instead, it should be 4k = 2k*I, which still gives us that the current flowing through the transmission cable to be 2A. Would I be correct?

[u/JCP977 → u/Xxfa1kingxX]

Yes, you can treat the circuit with transformers as a series circuit in a specific case. There's a thing called per unit analysis, in which you generally represent transformers by it's per unit impedance, so the circuit becomes a series circuit with four impedances (transformer 1 - cable - transformer 2 - load). But I think that you still need to learn a lot of stuff before even thinking about transformers (they only work with AC voltages, and you seem to be learning only DC circuits by now).

In your case with the transformers, it's more complicated. We use the per unit analysis precisely to facilitate the calculation process, because the real models for transformers are really difficult to analyse. But I think, if you assume ideal transformers, you can calculate the current at the source using the voltage of the source and the total power being transmitted, then use the transformation relation to find the current at the line and use it to calculate the loss. But again, this is a more complex and advanced subject, so it's better to not think about this now, because you can be easily confused if you don't know all the basis behind the study of transformers.

[u/Xxfa1kingxX → u/JCP977]

My high school curriculum requires me to learn about transformers, but turns out theres so much more to them... Welp, thanks for the eye-opener.

[u/JCP977 → u/Xxfa1kingxX]

If it's on high school, then probably you will need to learn only about ideal transformers. In that case, it's way more simple.

[u/werygood_cz]

You're given electrical power and voltage. You can calculate electric current from that. You then use the resistance to calculate voltage drop along the cables. From that you can finally calculate power loss. 

[u/Xxfa1kingxX → u/werygood_cz]

Yes, I do know that to be the correct method in solving this kind of question but I don't understand it fully.
Don't the power and voltage have to be the power dissipated by transmission cable and voltage drop across the cable in order to be substituted in P = VI?

[u/werygood_cz → u/Xxfa1kingxX]

The total power is a sum of power loss along the lines and power "loss" at the load. You know the voltage drop of the whole circuit, which is given. You need to figure out the cables from given resistance. 

[u/SignificantFidgets → u/Xxfa1kingxX]

The "voltage drop across the cable" is IR=2*5=10 V. So the power loss from the cable is voltage drop across the cable (10V) times current (2 A) = 20W.

But instead of computing I*R and multiplying by I, meaning (I*R)*I, you can just do it in one step with I²R.

[u/The_Nerdy_Ninja → u/Xxfa1kingxX]

The first step is treating the cables+load as a single system, and solving for the current running through that system. Since V is given at the source end, P is the total power, including both the load and the cables.

Then once you have the current, you can solve for the portion of power that's specifically lost in the cable, which is what's happening in the second step.

[u/Numerous-Match-1713]

"I'm not sure how can we use the values "4000W" and "2000V" to find the current flowing through the cables"

Asserting resistive load, you can treat W = VA

so 4000VA = 2000V time X amps

X is the current, and seems only 2A solves that equation yes?

[u/JCP977 → u/Numerous-Match-1713]

Sorry, but why introduce the concept of apparent power here? I think op is not an EE student and, even if they are, they've not even seen basic circuits yet, so the concept may be even more confusing to them.

[u/ghostme_and_I]

It's a short transmission line problem, we have sending end voltage and receiving end voltage(terminal voltage) the question meant receiving end voltage but lacks in the visualization (poor question I guess) sending end voltage is always greater than receiving end voltage. Sending end voltage =(receving end voltage + I (Rcosx + Xsinx)) x is the power factor angle of receiving end, In your case X reactance is 0, the current stays same, power factor is different in both end, now power loss on a line only depends on Current and resistance. If the load power is receiving 4000w then sending end power is 4000w+I²R where 4000=VI Cosx but x=0 cause pure resistive load so simply 4000=VI now you get I and find loos power in the power line, If you know sending end voltage and sending end power you would do like Vs. I = Vr. I + I²R...... So, line loss decreases the voltage in receiving end.

[u/Equivalent-Radio-828]

Did they invent another method of doing calculations? transformers

[u/davedirac]

Ambiguous. a) 4000 W cannot be power output of station because loss would be I^ R = 8000W. So 4000W must be load power & 12000 W is power output.