Inductor, capacitor and resistor in series in an ac circuit.

  Now let's take a look at an ac driven circuit containing a capacitor, inductor and resistor in series. The voltage V_R across the resistor will simply be proporional to the current. The charge on the capacitor, and therefore its voltage V_C will integrate the current as charges delivered by the current start collecting on the capacitor plates. The inductor on the other hand opposes changes in the current, and therefore its voltage V_L will be proportional to the derivative of the curent. If the current, which is has the same value throughout the entire circuit at any given time, is sinusoidal, then V_C will lag behind the current by 90 degrees and V_L will lead the current by 90 degrees. You can see this by integrating/differentiating a sine function. It is not surprising the V_C and V_L are 180 degrees out of phase. For example, consider the case when a current flows to charge the capacitor, increasing V_C to a positive value. At that same time, the inductor will try to oppose this increasing current, producing a negative V_L. The inductor is always opposing the currents that are charging/discharging the capacitor, so V_C and V_L are always 180 degrees out of phase.

  As can be seen in the applet below, it is clear that the applied voltage V_app is simply the vector sum of V_R, V_C, and V_L. Click on the "Show Current" button in the applet below to see the current flowing in this circuit. You should first carefully examine the voltages across each element before showing the current, which can complicate the picture.

  Since the impedances of inductors and capacitors depends on the driving frequency, V_L and V_C will change, which in turn will change the phase shift between the driving voltage V_app and the resulting current I, when the driving frequency changes. Try changing the frequency in the applet below. Notice what happens to the current when either frequency, C, or L are adjusted so that V_L exactly cancels V_C.

Use the above simulation to answer the following questions?