Instantaneous and Average Power Calculation in Sinusoidal Functions

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In this assignment, we explore the relationship between voltage and current in a sinusoidal system. Given the voltage function ( v(t) = 0.5 cos(4pi t) ) and the current function ( i(t) = 0.1 cos(4pi t) ), we aim to determine the instantaneous power ( p(t) ) at specific time points ( t = 0 ) and ( t = 0.25 ) seconds. Additionally, we will calculate the average power ( p_{av} ) over one full period of the cosine function, spanning from ( 0 ) to ( 0.5 ) seconds.

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Feb 20, 2026

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Instantaneous and Average Power Calculation in Sinusoidal Functions

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Section 2: Sinusoidal functions: Instantaneous current, voltage, power,
Assignment:1 • . The problem statement, all variables and given/known dataThe voltage across and current through a certain device are given by:v(t) = 5cos(4*pi*t)i(t) = .1cos(4*pi*t)Determine:(a) the instantaneous power p(t) at t= 0 and t = .25 seconds(b) the average power pav, defined as the average value of p(t) over a full time period of the cosine function (0 to .5 seconds)