Remove the inductor from the circuit in the figure and set $R=400 \mathrm{\Omega }, C=15.0 \mathrm{\mu F}, f_{\mathrm{d}}=30.0 \mathrm{Hz},$ and ${\mathcal{E}}_{\mathrm{m}}=72.0 \mathrm{V}.$ What are
(a)$Z,$ (b) $\varphi ,$and
(c) $I ?$
(d) Draw a phasor diagram.

Figure shows a driven $RLC$ circuit that contains two identical capacitors and two switches. The emf amplitude is set at $12.0 \mathrm{V},$ and the driving frequency is set at $60.0 \mathrm{Hz}.$ With both switches open, the current leads the emf by $25.0°.$ With switch $S_1$, closed and switch $S_2$ still open, the emf leads the current by $20.0°$ . With both switches closed, the current amplitude is $447 \mathrm{mA}$ . What are $\left(\mathrm{a}\right) R,\left(\mathrm{b}\right) C,$ and $\left(\mathrm{c}\right) L?$ Take $\tan \left(20°\right)=0.364$ and $\tan \left(25°\right)=0.466$

In $RLC$ an circuit, assume that $R=12.0 \mathrm{\Omega }$, $L=60.0 \mathrm{mH}, f_d=60.0 \mathrm{Hz},$ and  ${\epsilon }_m=30.0 \mathrm{V}.$ For what values of the
capacitance would the average rate at which energy is dissipated in the resistance be (a) a maximum and (b) a minimum? What are
(c) the maximum dissipation rate and the corresponding
(d) phase angle and (e) power factor? What are (f) the minimum dissipation rate and the corresponding
(g) phase angle and (h) power factor?

An alternating emf source with a variable frequency $f_{\mathrm{d}}$ is connected in series with a $50.0 \mathrm{\Omega }$ resistor and a $28.0 \mathrm{\mu F}$ capacitor. The emf amplitude is $12.0 \mathrm{V}$ .

(a) Draw a phasor diagram for $V_{\mathrm{R}}$ phasor (the potential across the resistor) and phasor $V_C$ (the potential across the capacitor).

(b) At what driving frequency $f_{\mathrm{d}}$ do the two phasors have the same length?

At that driving frequency, what are
(c) the phasor angle in degrees,

(d) the angular speed at which the phasors rotate, and

(e) the current amplitude?

 A $85.0 \mathrm{mH}$ inductor is connected as in the figure, to an $AC$ generator with ${\mathcal{E}}_m=30.0 \mathrm{V}$. What is the amplitude of the resulting alternating current if the frequency of the emf is
$\left(a\right) 1.00 \mathrm{kHz}$ and $\left(b\right)$ $5.00 \mathrm{kHz}$?