|Voltage and Current in AC Circuits|
In this problem, we consider the behavior of resistors, inductors, and capacitors driven individually by a sinusoidally alternating voltage source, for which the voltage is given as a function of time by . The main challenge is to apply your knowledge of the basic properties of resistors, inductors, and capacitors to these "single-element" AC circuits to find the current through each. The key is to understand the phase difference, also known as the phase angle, between the voltage and the current. It is important to take into account the sign of the current, which will be called positive when it flows clockwise from the b terminal (which has positive voltage relative to the a terminal) to the a terminal (see figure). The sign is critical in the analysis of circuits containing combinations of resistors, capacitors, and inductors.
Learning Goal: To understand the relationship between AC voltage and current in resistors, inductors, and capacitors, especially the phase shift between the voltage and the current.