Question

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

Answer 1

Step 1: Given data

Voltage: $V=220V$

Frequency: $f=50Hz$

The time taken for the complete cycle is $T$, which is the time period of the cycle. The time taken by half cycle will be $\frac{T}{2}$. And the time taken to reach to the peak value from zero will be $\frac{T}{4}$ as it is equal to one-fourth of the complete cycle.

Step 2: Formula Used

$T=\frac{1}{f}$

$t=\frac{T}{2}-\frac{T}{4}=\frac{T}{4}$, where $T$ is the time period, $t$ is the time taken to reach zero from the peak and $f$ is the frequency.

Step 3: Calculate the time to change from peak value to 0.

Calculate the time period using the formula

$$\begin{gathered} T=\frac{1}{f} \\ =\frac{1}{50Hz} \\ =0.02s \end{gathered}$$

Calculate the time to reach 0 from the peak by using the formula

$$\begin{gathered} t=\frac{T}{4} \\ =\frac{0.02s}{4} \\ =5\times {10}^{-3}s \end{gathered}$$

Hence, the time taken for voltage to change from its peak value to zero is $5\times {10}^{-3}s$.