Sketch Current Energy from 0 to 2T

In summary, the conversation discussed the process of finding the energy from t = 0 to t = 2T using the given waveform and given values for R and i. The formula for calculating energy was used, and the resulting graph showed a line with positive slope indicating an increase in energy over time. The concept of energy not being created or destroyed was also emphasized.
  • #1
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From the given waveform (of current), sketch the energy from t = 0 to t = 2T. Given: R = 10 Ohms, i = 10 Amps
mhxeh4.jpg


I'm having trouble with this even though it's probably really easy.
I know WR = ∫Ri2(t) dt
so for one period, for example, I have
∫10(102) dt with limits of integration from 0 to T/2
= 1000 t / t goes from 0 to T/2
= 500T
i believe this is a line with slope 500 going from 0 to T/2..but I'm not sure what i do for the other values of t
when i graph it should I just graph 1000t and plug in values for t?
 
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  • #2
Energy = time integral of power.

So you're doing just fine up to T/2.

Question to you: given the above, what should the curve look like between T2 and T?

And when the second pulse starts, until 3T/2?
And from 3T/2 to 2T?
 
  • #3
i would assume it just repeats, and from T/2 to T it would be zero and again from 5T/2 to 3T. but would it be somewhat like a sawtooth wave?
 
  • #4
Why would it be zero from T/2 to T? Where did the energy go?

BTW the problem doesn't ask you to go beyond 2T so I wouldn't.
 
  • #5
magnifik said:
from T/2 to T it would be zero
When I is zero then additional energy dissipated as heat in the resistor would be zero. Note: additional energy during T/2 -> T is zero.
 
  • #6
NascentOxygen said:
When I is zero then additional energy dissipated as heat in the resistor would be zero. Note: additional energy during T/2 -> T is zero.

why additional? what other energy is there? or where does it come from?
i only know of energy being equal to ∫p dt = ∫ Ri2(t) dt, and isn't p 0 from T/2 to T?
 
  • #7
Magnifik -please - for the last time - the energy you built up from 0 to T/2 has not disasppeared, so your graph just HAS to show it! Energy cannot be created or destroyed!

Yes - P is zero, but E is not, it's what it was at t = T/2 -.
 
  • #8
It's a resistor, so we are not talking about some vague concept or interplay of various energy forms. We are talking HEAT. Total heat energy. It's a graph that keeps increasing (never dropping) because it is a plot summing total heat energy since time t=0.
 
  • #9
i'm still confused as to what the graph would look like.
is the total energy delivered over one period 500T? ... i think i just understood why T/2 to T is not 0 with that question
 
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  • #10
magnifik said:
i'm still confused as to what the graph would look like.
is the total energy delivered over one period 500T? ... i think i just understood why T/2 to T is not 0 with that question

Let me try an analogy. You have a 100W light bulb. You turn it on for 1/2 hour and then turn it off for the next half hour.

Now graph what the watt-hour meter reads during the 1 hour time period.
 
  • #11
rude man said:
Let me try an analogy. You have a 100W light bulb. You turn it on for 1/2 hour and then turn it off for the next half hour.

Now graph what the watt-hour meter reads during the 1 hour time period.

It would be 50 watt-hour for the hour long time period. then the next hour would be 50 again so total would be 100, etc., etc.
if i plotted it over time, it would be a line with positive slope, yes?
 
  • #12
magnifik said:
It would be 50 watt-hour for the hour long time period. then the next hour would be 50 again so total would be 100, etc., etc.
if i plotted it over time, it would be a line with positive slope, yes?

I asked for just the 1 hour interval.

No, it would read 100t watt-hours during the first 30 minutes and 50 watt-hrs after that until 1 hr. t is in hours.
 
  • #13
rude man said:
I asked for just the 1 hour interval.

No, it would read 100t watt-hours during the first 30 minutes and 50 watt-hrs after that until 1 hr. t is in hours.

Woops, misread your question. I thought you meant it was already on for 30 minutes and then off for the next 30 minutes so the power was like a pulse train.

I thought for energy
It's a graph that keeps increasing (never dropping) because it is a plot summing total heat energy since time t=0.
 
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  • #14
magnifik said:
Woops, misread your question. I thought you meant it was already on for 30 minutes and then off for the next 30 minutes so the power was like a pulse train.

That is what I meant. The bulb is on for 0< t < 30 min. and off for 30 < t < 1 hr.

I thought for energy
It's a graph that keeps increasing (never dropping) because it is a plot summing total heat energy since time t=0.

Now you're cooking with gas - or whatever your electric utility burns! :-)
 

1. What is the significance of sketching current energy from 0 to 2T?

The graph of current energy over time can provide insights into the behavior of an electrical circuit or device. By sketching from 0 to 2T, we are able to see the initial behavior of the current and how it changes over time.

2. How can I sketch current energy from 0 to 2T?

To sketch current energy from 0 to 2T, you will need to plot the current values on the y-axis and time values on the x-axis. Start at 0 on the x-axis and plot the corresponding current value. Then, continue plotting the current values at regular intervals until you reach 2T on the x-axis.

3. What does the shape of the current energy graph tell us?

The shape of the current energy graph can tell us about the behavior of the electrical circuit or device. For example, a steep increase in current energy may indicate a sudden surge of power, while a gradual increase may indicate a steady flow of electricity.

4. What are some factors that can affect the current energy graph?

The current energy graph can be affected by various factors such as the type of circuit or device, the resistance and capacitance of the circuit, and external factors like temperature or interference. It is important to consider these factors when interpreting the graph.

5. How can current energy from 0 to 2T be used in practical applications?

The graph of current energy from 0 to 2T can be used in various practical applications, such as analyzing the performance of electrical devices, troubleshooting circuit issues, and predicting the behavior of a circuit over time. It can also be used for designing and optimizing circuits for specific purposes.

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