A circuit with capacitance `C` and inductance `L` generates free damped oscillations with current varying with time as `I=I_(m)e^(-betat) sin omegat`. Find the voltage across the capacitor as a function of time, and in particular, at the moment `t=0`.

Find how the voltage across the capacitor C varies with time t after closing of the switch S_(w) at the moment t=0 . .

In the circuit shown the source voltage is given as v = V_(0) sin omegat . Find the current through the source as a function of time.

An oscillating circuit consisting of a capacitor with capacitance C and a coil of inductance L maintans free undamped oscillations with voltage amplitude across the capacitor equal to V_(m) . For an arbitrary moment of time find the relation between the current I in the circuit and the voltage V acroos the capacitor. Solve this problem usdini Omega 's law and then the energy conservation law.

A circuit consisting of a capacitor with capacitance C and a resistance R connected in series was connected at the moment t=0 to a source of ac voltage V=V_(m) cos omegat . Find the current in the circuit as a function of time t .

Figure shows the variation of voltage with time for an ac I=I_(0) sin omegat flowing through a circuit -

A point performs dampled oscillations according to the law x=a_(0)e^(-betat)sin omegat . Find : (a) the oscillation amplitude and the velocity of the point at the moment t=0 , (b) the moments of time at which the point reaches the extreme positions.

A small signal voltage V(t)=V_0 sin omegat is applied across an ideal capacitor C:

Find the rms value of current from t = 0 to t=(2pi)/omega if the current varies as i=I_(m)sin omegat .