The current amplitude $I$ versus driving angular frequency, ${\omega }_{\mathrm{d}}$  for a driven $RLC$ circuit is given in the figure where the vertical axis scale is set by, $I_{\mathrm{s}}=4.00 \mathrm{A}$ . The inductance is $450 \mu \mathrm{H},$ and the emf amplitude is $6.0 \mathrm{V}.$ What are $\left(\mathrm{a}\right) C$ and $\left(\mathrm{b}\right) R$? 

 

An $RLC$ circuit such as that of figure, $R=5.00 \mathrm{\Omega }$ has $C=20.0\text{ μF}, L=2.00 \mathrm{H},$ ${\epsilon }_{\mathrm{m}}=30.0 \mathrm{V}.$ and (a) at what angular ${\omega }_{\text{d}}$ frequency will the current amplitude have its maximum value as in the resonance curves of given figure? (b) What is this maximum value? At what (c) lower angular frequency ${\omega }_{\text{d}1}$ and (d) higher angular frequency ${\omega }_{\text{d}2}$ will the current amplitude be half this maximum value?
(e) For the resonance curve for this circuit, what is the fractional half-width $\left({\omega }_{\text{d}1}-{\omega }_{\text{d}2}\right)/\omega ?$

 An alternating source with a variable frequency, an inductor with inductance  $L,$ and a resistor with resistance $R$ are connected in series. Below figure gives the impedance $Z$of the circuit versus the driving angular frequency  ${\omega }_{\mathrm{d}},$ with the horizontal axis scale set by ${\omega }_{\mathrm{ds}}=1600 \mathrm{rad} {\mathrm{s}}^{-1}.$ The figure also gives the reactance $X_{\mathrm{L}}$ for the inductor versus ${\omega }_{\mathrm{d}}.$ What are $\left(\mathrm{a}\right) R$and $\left(\mathrm{b}\right) L?$ 

The frequency of oscillation of a certain $LC$  circuit is $200 \mathrm{kHz}.$ At time $t=0,$ plate $A$ of the capacitor has maximum positive charge. At what earliest  time  $t>0$ will

(a) plate $A$ again have maximum positive charge, (b) the other plate of the capacitor have maximum positive charge, and (c) the inductor have maximum magnetic field?