In an RLC series circuit that includes a source of alternating current operating at fixed frequency and voltage, the resistance R is equal to the inductive reactance. If the plate separation of the parallel-plate capacitor is reduced to one-half its original value, the current in the circuit doubles. Find the initial capacitive reactance in terms of R.

An alternating source with a variable frequency, a capacitor with capacitance C, and a resistor with resistance Rare connected in series. The figure gives the impedance Z of the circuit versus the driving angular frequency Wa; the curve reaches an asymptote of 635 Q, and the horizontal scale is set by wds = 348 rad/s. The figure also gives the reactance Xc for the capacitor versus wd. What are (a) R and (b) C? Assume Z, - 508 Q. w (rad/s) (a) Number i Units (b) Number i Units (73) 'x Z

A current of I(t) = (5.50 mA)((sin(325 s-1)t ) passes through a 38 microF capacitor. What is the rms voltage across the capacitor?

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.