Electrical oscillations are initiated in a series circuit containing a capacitance C, inductance L, and resistance R. (a) If R << sqrt4L/C (weak damping), what time interval elapses before the amplitude of the current oscillation falls to 50.0% of its initial value? (b) Over what time interval does the energy decrease to 50.0% of its initial value?

The current in an Series RL circuit is described by the following differential equation:R i(t) + L di(t)/(dt) = V0where R is the resistance, L is the inductance, and V0 is the voltage of the source. a) Show that this is a separable differential equation, and then solve it. (Find i(t) in terms of R, L, V0). b) For a Series RL circuit with R = 50 (Ohm) and L = 10 (Henry) and the constant voltage V0 = 100 (Volt) applied at t = 0 by closing of a switch, find the current at t = 0.5 second.

(a) If an inductor carrying a 1.95 A current stores an energy of 0.250 mJ, what is its inductance? Answer in mH (b) How much energy does the same inductor store if it carries a 3.1 A current? Answer in mJ

A circuit consists of a 20 nF capacitor in series with a 20 µH inductor. If a charge of 30 nC is put on the capacitor, there is an oscillation. (a) What is the maximum current that moves through the circuit? (b) Find the maximum energy in the inductor and the in the capacitor? (c) What is the angular frequency of oscillation? What is the period? (d) Assume the trace resistance in the circuit is 0.102. Describe quantitatively and qualitatively the oscillation in the circuit.