EXERCISE 10

A series LCR circuit is connected to an ac source having voltage $v=v_m\sin \omega t$. Derive the expression for the instantaneous current $I$ and the phase relationship to the applied voltage. Obtain the condition for resonance to occur. Define power factor. State the conditions under which it is

(i) Maximum,

A series LCR circuit is connected to an ac source having voltage $v=v_m\sin \omega t$. Derive the expression for the instantaneous current $I$ and the phase relationship to the applied voltage. Obtain the condition for resonance to occur. Define power factor. State the conditions under which it is

(ii) Minimum.

A series $\mathrm{R}-\mathrm{C}$ circuit is connected to $\mathrm{AC}$ voltage source. Consider two cases $\left(\mathrm{A}\right)$ When $\mathrm{C}$ is without a di-electric medium and $\left(\mathrm{B}\right)$ when $\mathrm{C}$ is filled with dielectric of constant $4$. The current ${\mathrm{I}}_{\mathrm{R}}$ through the resistor and voltage ${\mathrm{V}}_{\mathrm{C}}$ across the capacitor are compared in the two cases. Which of the given option is correct?

A fully charged capacitor $\mathrm{C}$ with initial charge ${\mathrm{q}}_0$ is connected to a coil of self-inductance $\mathrm{L}$ at $\mathrm{t}=0$. The time at which the energy is stored equally between the electric and magnetic fields is

Find the phase-difference between the current and the voltage, If in a series $\mathrm{L}-\mathrm{C}-\mathrm{R}$ circuit, resistance $\mathrm{R}=10 \mathrm{\Omega }$ and the impedance $\mathrm{Z}=10 \mathrm{\Omega }$.

In L-C-R circuit as shown in figure, both switches are open initially. Now switch ${\mathrm{s}}_1$ and ${\mathrm{s}}_2$ are closed. ($\mathrm{q}$ is charge on the capacitor and $\mathrm{\tau }=\mathrm{RC}$ is capacitance time constant) which of the following statement is correct?

In the circuit shown in Fig. there are two parallel plate capacitors each of capacitance $\mathrm{C} .$ The switch $S_1$ is pressed first to fully charge the capacitor ${\mathrm{C}}_1$ and then released. The switch ${\mathrm{S}}_2$ is then pressed to charge the capacitor ${\mathrm{C}}_2.$ After sometime, ${\mathrm{S}}_2$ is released and then ${\mathrm{S}}_3$ is pressed. After some time
  

In the given circuit, the $\mathrm{AC}$ source has $\mathrm{\omega }=100$ $\mathrm{rad}/\mathrm{c}$. Considering the inductor and capacitor to be ideal, the correct choice (s) is (are)