Chapter 8, Problem 33P

Figure P8.33 shows a circuit with a resistor, an inductor, and a capacitor in parallel. Kirchhoff's rules can be used to express the impedance of the system as

$\frac{1}{Z}=\sqrt{\frac{1}{R^2}+{\left(\omega C-\frac{1}{\omega L}\right)}^2}$

where $Z=$ impedance $\left(\Omega \right)\text{ and }\omega =$ the angular frequency. Find the $\omega$ that results in an impedance of 75 $\Omega$ using both bisection and false position with initial guesses of 1 and 1000 for the following parameters: $R=225\Omega ,C=0.6\times {10}^{-6}\text{F, and }L=0.5\text{H}$. Determine how many iterations of each technique are necessary to deter-mine the answer to ${\epsilon }_s=0.1\%$. Use the graphical approach to explain any difficulties that arise.

FIGURE P8.33