Why is power loss = I^2R instead of P=VI or P=I^2R?

In summary, the power station generates 120kW of power at an EMF of 240 V. It is transmitted 10 km away through 0.40 ohm transmission lines. To calculate the current in the transmission lines, we can use the formula P=VI, where P is the power, V is the voltage, and I is the current. Plugging in the values, we get I = P/V = 120kW / 240V = 500 A. 2) To find the voltage drop across the transmission lines, we can use Ohm's Law which states that V=IR, where V is the voltage, I is the current, and R is the resistance. Plugging in the
  • #1
victorhugo
127
5
[Moderator note: Thread moved from technical section hence no template. Question text from later in the thread added to this post to make things clear]

"A power station generates electric power at 120kW. It sends this power to a town 10 km away through transmission lines that have a total resistance of 0.40 ohms. If the power is transmitted at 240 V, calculate:

a. the current in the transmission lines
b. the voltage drop across the transmission lines
c. the power loss in the transmission lines
d. the power loss in the transmission lines "

[Since question d looks an awful lot like question c, I suspect a miscopy from the original source]

Since power is in joules, i'd imagine we could get the energy in - energy out (using p=vi=i^2r).
But it doesn't work like that. My textbook states that power loss = I^2R, but why?
Could someone explain please? thank you
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
victorhugo said:
Since power is in joules
The unit of power is Watts... :smile:
 
  • #3
berkeman said:
The unit of power is Watts... :smile:
Oh... Oops.
 
  • #4
so e=pt?
 
  • #5
also i still don't see the process where i can get power loss by I^2R...
 
  • #6
victorhugo said:
so e=pt?
Yes, Energy = Power * Time
victorhugo said:
also i still don't see the process where i can get power loss by I^2R...
Can you say more about your specific question? The energy loss in wires leading to a load is I^2 * R.
 
  • #7
"A power station generates electric power at 120kW. It sends this power to a town 10 km away through transmission lines that have a total resistance of 0.40 ohms. If the power is transmitted at 240 V, calculate:

a. the current in the transmission lines
b. the voltage drop across the transmission lines
c. the power loss in the transmission lines
d. the power loss in the transmission lines "

I haven't gone over this stuff in a veryyy long time but it helps to understand it for my last course. I honestly don't get the way they do *any* of those questions, so a logical explanation to any assumed knowledge would definitely help :)
 
  • #8
*btw this is not homework but me revising some basic stuff i need to know for my upcoming course*
 
  • #9
You have been here long enough to know that all schoolwork-type questions go in the Homework Help forums, and use the HH Template. Sigh.
 
  • #10
berkeman said:
You have been here long enough to know that all schoolwork-type questions go in the Homework Help forums, and use the HH Template. Sigh.
Well it's been a while since i had to trouble doing homework questions so it didnt even pop into mind.
"A power station generates electric power at 120kW. It sends this power to a town 10 km away through transmission lines that have a total resistance of 0.40 ohms. If the power is transmitted at 240 V, calculate:

a. the current in the transmission lines
b. the voltage drop across the transmission lines
c. the power loss in the transmission lines
d. the power loss in the transmission lines "

a. I don't like to pick out the formulas i have and plug in the numbers I have. I want to see how the formula works. So, current being C/s, I don't see what i can do here.
same for b, c and d.
please help :frown:
 
  • #11
victorhugo said:
Well it's been a while since i had to trouble doing homework questions so it didnt even pop into mind.
"A power station generates electric power at 120kW. It sends this power to a town 10 km away through transmission lines that have a total resistance of 0.40 ohms. If the power is transmitted at 240 V, calculate:

a. the current in the transmission lines
b. the voltage drop across the transmission lines
c. the power loss in the transmission lines
d. the power loss in the transmission lines "

a. I don't like to pick out the formulas i have and plug in the numbers I have. I want to see how the formula works. So, current being C/s, I don't see what i can do here.
same for b, c and d.
please help :frown:
You are given the power input and the resistance of the transmission line. What is the current to deliver that power at that voltage? What would be the power dissipated in the wires to deliver that current?
 
  • #12
We actually get power from
$$ P = εI $$
where ε is the emf. ε is the energy per unit charge. Current is the charge passing through per unit time. Therefore, the product of them means how much energy is passing through per unit time. You also have the relation between I, ε, R. You can then find the answer you want
 
  • #13
Chan Pok Fung said:
We actually get power from
$$ P = εI $$
where ε is the emf. ε is the energy per unit charge. Current is the charge passing through per unit time. Therefore, the product of them means how much energy is passing through per unit time. You also have the relation between I, ε, R. You can then find the answer you want
That's not helpful in this question.

Quiz Question -- Why not? :smile:
 
  • #14
Chan Pok Fung said:
We actually get power from
$$ P = εI $$
where ε is the emf. ε is the energy per unit charge. Current is the charge passing through per unit time. Therefore, the product of them means how much energy is passing through per unit time. You also have the relation between I, ε, R. You can then find the answer you want
berkeman said:
That's not helpful in this question.
Actually it can help if @victorhugo considers this fundamental enough to start with. The current delivered by the power source can be extracted from the source EMF and the power it generates, both given values:
victorhugo said:
"A power station generates electric power at 120kW... If the power is transmitted at 240 V...
So the power station is putting out 120 kW with an EMF of 240 V.
 
  • Like
Likes Mayan Fung
  • #15
In short the issue is P(w) = V(v) * I(a) Since V= I * R(ohms) we have
=( I * R ) * I = I^2R.

In this problem - for clarity it should state this is a single phase system, and V and I units in RMS values.
 

1. What is the equation for power loss in a circuit?

The equation for power loss in a circuit is P = I^2R, where P represents power in watts, I represents current in amperes, and R represents resistance in ohms.

2. Why is the power loss formula written as P = I^2R?

The power loss formula is written as P = I^2R because it is derived from Ohm's Law, which states that voltage is equal to current multiplied by resistance (V = IR). By substituting this equation into the formula for power (P = VI), we get P = I^2R.

3. How does increasing current affect power loss?

Increasing current in a circuit will result in a higher power loss because according to the power loss formula (P = I^2R), the power loss is directly proportional to the square of the current. This means that a small increase in current will result in a larger increase in power loss.

4. How does resistance impact power loss?

Resistance has a direct effect on power loss in a circuit. As resistance increases, power loss also increases because according to the power loss formula (P = I^2R), the power loss is directly proportional to the resistance. This means that a higher resistance will result in a higher power loss.

5. Can the power loss formula be used to calculate power consumption?

Yes, the power loss formula can be used to calculate power consumption. By using the formula P = I^2R, we can calculate the power lost in a circuit and then subtract it from the total power input to determine the power consumption. This is useful for understanding the efficiency of a circuit or device.

Similar threads

Power Line Losses: Trivial Problem, Confusing Answer
    • Introductory Physics Homework Help
Replies
9
Views
1K
Long distance electrical transmission efficiency
    • Introductory Physics Homework Help
Replies
2
Views
755
Power loss in transmission lines
    • Introductory Physics Homework Help
Replies
20
Views
9K
Power loss in the transmission system with a transformer
    • Introductory Physics Homework Help
Replies
4
Views
1K
How transmission lines deliver (established?) power from generator
    • Electrical Engineering
Replies
8
Views
1K
Optimizing Voltage for Power Transmission Efficiency
    • Introductory Physics Homework Help
Replies
4
Views
3K
Power Loss, Current, Resistors, and Voltage
    • Introductory Physics Homework Help
Replies
4
Views
1K
Exploring Transformers: I^2R Power Losses
    • Introductory Physics Homework Help
Replies
4
Views
11K
Finding the Power Loss Through a Transmission Line
    • Introductory Physics Homework Help
Replies
4
Views
2K
P = VI = (281V)(3.75A) = 1054 W
    • Introductory Physics Homework Help
Replies
6
Views
7K

Hot Threads

Recent Insights

Back
Top