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GUJCET · Physics · Alternating Current
Find the time required for a 50 Hz alternating current to become its value from zero to the rms value.
- A 2.5 ms
- B 5.0 ms
- C 10.0 ms
- D 15.0 ms
Answer & Solution
Correct Answer
(A) 2.5 ms
Step-by-step Solution
Detailed explanation
(A) 2.5 ms
\(i=i_{m} \sin \omega t\)
\(
\begin{array}{rlrl}
\frac{i}{i_{m}} =\sin \omega t\left(\because \frac{i}{i_{m}}=\frac{1}{\sqrt{2}}\right) \end{array}
\)
\(
\begin{array}{rlrl} \therefore \frac{1}{\sqrt{2}} =\sin \omega t \\
\therefore \omega t =\frac{\pi}{4} \\
\therefore 2 \pi v t =\frac{\pi}{4} \\
\therefore t =\frac{1}{8 v} \\
\therefore t =\frac{1}{8 \times 50} \\
\therefore t =\frac{1}{400} \\
\therefore t =2.5 \mathrm{~ms}
\end{array}
\)
\(i=i_{m} \sin \omega t\)
\(
\begin{array}{rlrl}
\frac{i}{i_{m}} =\sin \omega t\left(\because \frac{i}{i_{m}}=\frac{1}{\sqrt{2}}\right) \end{array}
\)
\(
\begin{array}{rlrl} \therefore \frac{1}{\sqrt{2}} =\sin \omega t \\
\therefore \omega t =\frac{\pi}{4} \\
\therefore 2 \pi v t =\frac{\pi}{4} \\
\therefore t =\frac{1}{8 v} \\
\therefore t =\frac{1}{8 \times 50} \\
\therefore t =\frac{1}{400} \\
\therefore t =2.5 \mathrm{~ms}
\end{array}
\)
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