Electrical Engineering - Energy Graph Question

[Larrytsai]

Homework Statement

Question number 3!, I attached it. Need help!

Figure 1 shows the current through and the voltage across a device. Find the total energy absorbed by the device fore the period 0<t<4.

Homework Equations

integral of p = energy
P=VI

The Attempt at a Solution

Just need the algorithm to solving these kinds of problems, I am kind of thrown off at the instantaneous change.

 

[mplayer]

One way you could think about this problem is by taking discrete intervals on the current graph and voltage graph and multiplying these values together. This will result in a graph that describes the power dissipation in the device over the given time interval. Then it will just be a matter of finding the area under the curve (integrating the resulting power function).

 

[Larrytsai]

Yeah I thought about that approach but when I look at the voltage it comepletely throws me off. I am able to break the current into 2 separate intervals with the function y1=25x and 0<t<2, y2=-25x 2<t<4, but for the voltage at t=2 its constant and I can't come up with a function to multply with my current.

 

[mplayer]

For the voltage between t=1 and t=3, the function describing the voltage is just a constant, or y=10.

 

[DeeNos]

To find the total energy absorbed by the device, we need to integrate the power (P) over the given time period (0<t<4). The power is given by the equation P=VI, where V is the voltage and I is the current.

First, we need to calculate the power at each point in time. Looking at the graph, we can see that the voltage and current are both changing over time. To find the power, we can use the formula P=VI. We can calculate the voltage and current at each time point by looking at the graph and using the given values.

For example, at t=1, the voltage is 4V and the current is 2A. Plugging these values into the equation P=VI, we get P=4V*2A=8W. We can repeat this process for each time point and calculate the power at each point.

Once we have the power at each time point, we can use the integral of power (P) to find the total energy absorbed by the device. The integral of power over time gives us the total energy absorbed. We can use the trapezoidal rule or any other numerical integration method to calculate the integral.

In this case, we have discrete data points, so we can use the trapezoidal rule. We can divide the time period (0<t<4) into smaller intervals and calculate the area under the curve for each interval. Then, we can sum up all these areas to get the total energy absorbed by the device.

In summary, to solve this problem, we need to:
1. Calculate the power at each time point using the formula P=VI.
2. Use numerical integration (such as the trapezoidal rule) to find the total energy absorbed by the device.