# Phasors introductory exercise

1. Dec 20, 2015

### okh

1. The problem statement, all variables and given/known data
In this circuit, find $i(t)$, knowing that $v_s= 2 \cos \left(w x+\frac{\pi }{2}\right)$, and that, at the source's frequency, $X_C= -1 Ω$ and $X_L = 1 Ω$.

2. Relevant equations
Basic phasors and dividers equations.
$Z_C = jX_C$
$Z_L = jX_L$

3. The attempt at a solution
I used dividers. The source divides between R and the parallel of C and the series of L and R.
$I=\frac{Z_C v_s \left(Z_L+R\right)}{\left(Z_L+R\right) \left(Z_C+Z_L+R\right) \left(\frac{Z_C \left(Z_L+R\right)}{Z_C+Z_L+R}+R\right)}$
Solving with $R=1, Z_c=-j, Z_l=j, v_s=2j$ I get $i(t)=\frac{2}{\sqrt{5}}*cos(wt+0.46)$, while the correct phase should be $-2.68$. Basically I get the symmetrical cosine wave with respect to the x axis.

2. Dec 20, 2015

### Staff: Mentor

I agree with your result. It seems that they took the given voltage source phase $\pi/2$ to be a negative phase shift for some reason.

3. Dec 20, 2015

### okh

Thank you. Yeah, that may be the reason.