$(8$ points$)$ In a home stereo system, low sound frequencies are handled by large "woofer" speakers, and high frequencies by smaller "tweeter" speakers. For the best sound reproduction, low$-$frequency currents from the amplifier should not reach the tweeter. One way to do this is to place a capacitor in series with the $10\mathrm{.}0$ resistance of the tweeter.

What value of C should be chosen so that the current through the tweeter at $100$ Hz is one fourth of its value at very high frequencies?