Question

When an AC voltage of 220 V is applied to the capacitor then,
This question has multiple correct options.
A. The maximum voltage between plates is 220 V
B. The current is in phase with the applied voltage
C. The charge on the plate is not in phase with the applied voltage
D. Power delivered to the capacitor per cycle is zero

Answer 1

Hint: Define an AC voltage. AC voltage means the alternating voltage which gives us the voltage with alternating polarity every equal interval of time. Obtain the mathematical expression for the peak voltage and find it. Find the relation between the phase of the current, voltage and charge. Obtain the expression for power over a complete cycle and find the value of the power.

Complete step by step answer:
AC means alternating current. An AC voltage means that a voltage which switches polarity after a fixed interval of time.
In this question, we have an AC voltage of 220V applied to a capacitor C.
So, we are given that the rms value of the root mean squared value of the voltage as 220V.
${{V}_{rms}}=220V$
The relation between the rms voltage and the peak voltage is given as,
${{V}_{P}}=\sqrt{2}\times {{V}_{rms}}$
So, the peak voltage between the plates of the capacitor will be,
${{V}_{P}}=\sqrt{2}\times 220V=311.13V$
Now, the charge on the plates of a capacitor is not in phase with the voltage applied to the capacitor.
Now, in the capacitor connected in an AC circuit, the voltage and the current have a phase difference. This phase difference is equal to ${{90}^{0}}$ . so, the current in the capacitor is not in phase with the applied voltage.
Now, the power delivered to the capacitor can be expressed in terms of the voltage and current of the capacitor as,
$P=IV\cos \theta $
Where, P is the power delivered to the capacitor, I is the current and V is the voltage.
$\theta $ is the phase difference between the current and voltage of the capacitor which is ${{90}^{0}}$.
So, the power delivered to the capacitor per cycle is,
$\begin{align}
  & P=IV\cos {{90}^{0}} \\
 & P=0 \\
\end{align}$

So, the correct options are (C) and (D).


Note:
AC voltage will give us periodically varying voltage over a fixed interval of time. A DC voltage will give us a fixed voltage. So, in case of AC voltage we have rms value, but in case of DC voltage we do not have rms value.