Combining the Impedances and Admittances

Problem-Solving Strategy for Combining the Impedances and Admittances

STEP 1. Add the admittances of elements in parallel.

STEP 2. Add the impedances of elements in series.

STEP 3. Convert back and forth between admittance and impedance in order to combine neighboring elements.

Note: This post is based on Irwin's Basic Engineering Circuit Analysis 11th ed.

If there are any errors in solution, please let me know in the comments

Since R, L, and C are connected in parallel, the admittance will be useful. The admittance of each element are

$\mathbf Y_R=\frac{1}{R}=1S$

$\mathbf Y_L=\frac{1}{jwL}=-j\frac{200}{w}S$

$\mathbf Y_C=jwC=j\frac{w}{1000}S$

So $\mathbf Y=1-j\frac{200}{w}+j\frac{w}{1000}S$

Purely resistive means $ -j\frac{200}{w}+j\frac{w}{1000}=0$, therefore

$w^2=200000$

$w=447.21 rad/s$

$f=71.18Hz$