Question

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

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Solution

## Step 1: Given dataVoltage: $V=220V$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$T=\frac{1}{f}\phantom{\rule{0ex}{0ex}}=\frac{1}{50Hz}\phantom{\rule{0ex}{0ex}}=0.02s$Calculate the time to reach 0 from the peak by using the formula$t=\frac{T}{4}\phantom{\rule{0ex}{0ex}}=\frac{0.02s}{4}\phantom{\rule{0ex}{0ex}}=5×{10}^{-3}s$Hence, the time taken for voltage to change from its peak value to zero is $5×{10}^{-3}s$.

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