Question

An AC source is rated at$220\;V$,$50\;Hz$. The time taken for voltage to change from its peak value to zero is:

Answer 1

Hint: We know that electrical current is of two types namely the AC or the alternating currents and the DC or the direct currents. We also know that in an AC, there is periodic change in direction and magnitude of the electrons which flow, thus accounting for the name AC.

Complete step-by-step solution:
AC is mostly described as the wave forms, they can either be sine waves or cosines waves. Thus during the positive half cycle, the current travels in the positive direction and has positive magnitude, while in the negative half cycle, the current travels in the negative direction with a negative value.
Then the voltage at any given instant $v(t)$ due to AC can be described as
$v(t)=V_p sin(\omega t)$, where $V_P$ is the peak or maximum voltage the AC source can provide with angular frequency $\omega$ at $t$time, as shown in the figure below.

Also,$V_p=\sqrt{2} V_{rms}$ where $V_{rms}$ is the square root of mean voltage over one cycle of the instantaneous voltage.
Since the peak voltage occurs at $t=\dfrac{T}{4}$ and min voltage which is $0$ occurs at $t=\dfrac{T}{2}$, we can say that the time the taken for AC voltage to fall from peak to zero as
$t=\dfrac{T}{2}-\dfrac{T}{4}=\dfrac{2T}{8}$
Given that the frequency of the AC source is $f=\dfrac{1}{T}=50\;Hz$
Thus, $t=\dfrac{2}{8\times 50}$
$\therefore t=5\times 10^{-3}s$
The time the taken for AC voltage to fall from peak to zero is $5\times 10^{-3}s$

Note: In a DC the electrons and thus the current flows only in one direction as compared to that of the AC. Also the current which we use in our houses are AC as AC shocks are comparatively less dangerous to that of DC shocks. The most common source of DC could be the battery cells which are used in remotes.