Find the time required for a 50Hz alternating current to change its value from zero to the rms value.
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$\text{f}=50\text{Hz}$
$=\text{I}=\text{I}_0\sin\omega\text{t}$
Peak value $\text{I}=\frac{\text{I}_0}{\sqrt{2}}$
$\frac{\text{I}_0}{\sqrt{2}}=\text{I}_0\sin\omega\text{t}$
$\Rightarrow\ \frac{1}{\sqrt{2}}=\sin\omega\text{t}=\sin\frac{\pi}{4}$
$\Rightarrow\ \frac{\pi}{4}=\omega\text{t}$
Or $\text{t}=\frac{\pi}{400}$
$=\frac{\pi}{4\times2\pi\text{f}}=\frac{1}{8\text{f}}$
$=\frac{1}{8\times50}=0.0025\text{s}=2.5\text{ms}$
$=\text{I}=\text{I}_0\sin\omega\text{t}$
Peak value $\text{I}=\frac{\text{I}_0}{\sqrt{2}}$
$\frac{\text{I}_0}{\sqrt{2}}=\text{I}_0\sin\omega\text{t}$
$\Rightarrow\ \frac{1}{\sqrt{2}}=\sin\omega\text{t}=\sin\frac{\pi}{4}$
$\Rightarrow\ \frac{\pi}{4}=\omega\text{t}$
Or $\text{t}=\frac{\pi}{400}$
$=\frac{\pi}{4\times2\pi\text{f}}=\frac{1}{8\text{f}}$
$=\frac{1}{8\times50}=0.0025\text{s}=2.5\text{ms}$
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