Chapter 10, Problem 14P

An RLC circuit with an alternating voltage source is shown. The source voltage v_sis given by $v_s=v_m\sin ({\omega }_{d}t)$ , where ${\omega }_d=2\pi f_d$ , in which f_dis the driving frequency. The amplitude of the current, I, in this circuit is given by:

$I=\frac{v_m}{\sqrt{R^2+[{\omega }_{d}L-1/{({\omega }_{d}C]}^2}}$ where R and C are the resistance of the resistor and capacitance of the capacitor, respectively. For the circuit in the figure $C=15\times {10}^{-6}$ F, $L=240\times {10}^{-3}$ H and v_m= 24V.

$60\le f\le 110$ Hz, and as a function of R (y axis) for $10\le R\le 40\Omega$ .

(b) Make a plot that is a projection on the x z plane. Estimate from this plot the natural frequency of the circuit (the frequency at which I is maxim um). Compare the estimate with the calculated value of $1/\left(2\pi \sqrt{LC}\right)$.