Graphing power p(t) with voltage v(t) and current i(t) given?

[elimenohpee]

I'm having a little trouble relating the graphs of voltage, current, and power together. I am given graphs of v(t) and i(t) and I need to sketch p(t). I know p(t) is (v*i), so do I need to integrate the slopes of the values for v(t) and i(t) under a definite integral (to get the discrete values) or to find the area of the curves of the graph, then multiply them together under (v*i)?

 

[Redbelly98]

Just multiply v and i. No integration, no derivatives, no calculus whatsoever.

 

[piercas]

Yes, you are correct in your understanding that power (p) is equal to voltage (v) multiplied by current (i). To sketch the graph of p(t), you can either integrate the slopes of the values for v(t) and i(t) under a definite integral, or find the area under the curves of the graphs and then multiply them together. Both methods will give you the same result.

To integrate the slopes, you can use the following formula:

p(t) = ∫v(t)*i(t) dt

Where ∫ represents the definite integral and dt represents the change in time. This will give you the discrete values of p at different points in time.

Alternatively, you can find the area under the curves of v(t) and i(t) and multiply them together to get the value of p at each point in time. This method is often used when the graphs are not continuous and have distinct data points.

Once you have calculated the values of p at each point in time, you can plot them on a graph to get the graph of p(t). This will show you how the power changes over time, based on the changing values of voltage and current.

In summary, to sketch the graph of p(t) using the given graphs of v(t) and i(t), you can either integrate the slopes or find the area under the curves and multiply them together. Both methods will give you the same result and show the relationship between voltage, current, and power over time.