Introduction:
In this problem, we are given an alternating voltage source with an angular frequency of 100V. This voltage is connected across a capacitor and an inductor. We need to find the ratio of the current through the inductor to the voltage source.

Explanation:

To solve this problem, we need to analyze the behavior of the capacitor and the inductor in an AC circuit. Both the capacitor and the inductor exhibit different responses to an alternating current compared to a direct current.

Capacitor:
A capacitor in an AC circuit behaves as an open circuit for DC signals, but for AC signals it allows the flow of current. The current through a capacitor in an AC circuit leads the applied voltage by 90 degrees.

Inductor:
An inductor in an AC circuit behaves as a short circuit for DC signals, but for AC signals it resists the flow of current. The current through an inductor in an AC circuit lags behind the applied voltage by 90 degrees.

Impedance:
Impedance is the opposition to the flow of alternating current. It is similar to resistance in a DC circuit. For a capacitor, the impedance is given by Zc = 1/(jωC), where j is the imaginary unit, ω is the angular frequency, and C is the capacitance. For an inductor, the impedance is given by ZL = jωL, where j is the imaginary unit, ω is the angular frequency, and L is the inductance.

Current through the inductor:
The current through the inductor can be calculated using Ohm's law for AC circuits. The current is given by I = V/ZL, where V is the voltage across the inductor and ZL is the impedance of the inductor.

Ratio of current through inductor to voltage source:
To find the ratio of the current through the inductor to the voltage source, we need to calculate the impedances of the inductor and the capacitor. Since the voltage source and the inductor have the same angular frequency, their impedances are directly proportional. Hence, the ratio of the current through the inductor to the voltage source is equal to the ratio of the impedance of the inductor to the impedance of the voltage source.

Conclusion:
In this problem, we have analyzed the behavior of a capacitor and an inductor in an AC circuit. We have found that the current through the inductor lags the applied voltage by 90 degrees and can be calculated using Ohm's law for AC circuits. The ratio of the current through the inductor to the voltage source is equal to the ratio of the impedance of the inductor to the impedance of the voltage source.