- #1

SumDood_

- 30

- 6

- Homework Statement
- Calculate the power in the given circuit

- Relevant Equations
- P=IV

Help me understand what I am missing. So this is the circuit:

Given:

##V_{RMS} = 120V##

##I_{RMS}= 10A##

##v=Re \{Ve^{jwt}\}##

##i=Re \{Ie^{j(wt-\psi)}\}##

(a) Calculate and sketch real and reactive power P and Q as a function of the angle ψ

(b) Calculate and sketch the instantaneous power

What I've done so far:

##V = 120\sqrt{2}cos(\omega t)##

##I = 10\sqrt{2}cos(\omega t-\psi)##

##

\begin{align*}

P = iv &= 120\sqrt{2}cos(\omega t) \cdot 10\sqrt{2}cos(\omega t-\psi) \\

&= 120\sqrt{2}\frac{1}{2}(e^{j\omega t}+e^{-j\omega t}) \cdot 10\sqrt{2}\frac{1}{2}(e^{j(\omega t-\psi)}+e^{-j(\omega t-\psi)}) \\

&= 600(e^{j\psi} + e^{-j\psi} + e^{j(2\omega t - \psi)} + e^{-j(2\omega t - \psi)}) \\

&= 2400(cos(2\omega t - \psi) + cos(\psi))

\end{align*}

##

I am not sure if the work I've done is correct. If it is, I don't understand how to differentiate P and Q from the solution I have worked out.

Any help is appreciated!

Given:

##V_{RMS} = 120V##

##I_{RMS}= 10A##

##v=Re \{Ve^{jwt}\}##

##i=Re \{Ie^{j(wt-\psi)}\}##

(a) Calculate and sketch real and reactive power P and Q as a function of the angle ψ

(b) Calculate and sketch the instantaneous power

What I've done so far:

##V = 120\sqrt{2}cos(\omega t)##

##I = 10\sqrt{2}cos(\omega t-\psi)##

##

\begin{align*}

P = iv &= 120\sqrt{2}cos(\omega t) \cdot 10\sqrt{2}cos(\omega t-\psi) \\

&= 120\sqrt{2}\frac{1}{2}(e^{j\omega t}+e^{-j\omega t}) \cdot 10\sqrt{2}\frac{1}{2}(e^{j(\omega t-\psi)}+e^{-j(\omega t-\psi)}) \\

&= 600(e^{j\psi} + e^{-j\psi} + e^{j(2\omega t - \psi)} + e^{-j(2\omega t - \psi)}) \\

&= 2400(cos(2\omega t - \psi) + cos(\psi))

\end{align*}

##

I am not sure if the work I've done is correct. If it is, I don't understand how to differentiate P and Q from the solution I have worked out.

Any help is appreciated!

Last edited: