The circuit in Fig. 9.1 has the following parameters: υ(t) = 4 cos (ωt + 60°) V and $Z =2\underline{ / 30^{\circ}} \Omega$ . We wish to determine equations for the current and the instantaneous power as a function of time and plot these functions with the voltage on a single graph for comparison.

HINT
Note that p(t) contains a dc term and a cosine wave with twice the frequency of υ(t) and i (t).

Question

The circuit in Fig. 9.1 has the following parameters: υ(t) = 4 cos (ωt + 60°) V and $Z =2\underline{ / 30^{\circ}} \Omega$ . We wish to determine equations for the current and the instantaneous power as a function of time and plot these functions with the voltage on a single graph for comparison.

HINT
Note that p(t) contains a dc term and a cosine wave with twice the frequency of υ(t) and i (t).

Accepted Answer

Since

[latex] I =\frac{4 \underline{/ 60^{\circ}} }{2 \underline{/ 30^{\circ}} } [/latex]
[latex] =2 \underline{/ 30^{\circ}} A[/latex]

then
i(t) = 2 cos (ωt + 30°) A

From Eq. (9.5) [latex] p(t)=\frac{V_{M} I_{M}}{2}\left[\cos \left( heta_{v}- heta_{i} ight)+\cos \left(2 \omega t+ heta_{v}+ heta_{i} ight) ight] [/latex],
p(t) = 4[cos (30°) + cos (2ωt + 90°)]
= 3.46 + 4 cos (2ωt + 90°) W
A plot of this function, together with plots of the voltage and current, is shown in Fig. 9.2. As can be seen in this figure, the instantaneous power has a dc or constant term and a second term whose frequency is twice that of the voltage or current.

Question 9.1: The circuit in Fig. 9.1 has the following parameters: υ(t) =...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions