WBJEE · Physics · Alternating Current
An alternating current in a circuit is given by \(I=20 \sin (100 \pi t+0.05 \pi)\) A. The r.m.s. value and the frequency of current respectively are
- A \(10 \mathrm{A}\) and \(100 \mathrm{Hz}\)
- B \(10 \mathrm{A}\) and \(50 \mathrm{Hz}\)
- C \(10 \sqrt{2} \mathrm{A}\) and \(50 \mathrm{Hz}\)
- D \(10 \sqrt{2}\) A and \(100 \mathrm{Hz}\)
Answer & Solution
Correct Answer
(C) \(10 \sqrt{2} \mathrm{A}\) and \(50 \mathrm{Hz}\)
Step-by-step Solution
Detailed explanation
Given, \(I=20 \sin (100 \pi t+0.05 \pi)\) The root mean square value of alternating \[ \text { current }=l_{\mathrm{ms}}=\frac{l_{0}}{\sqrt{2}}=\frac{20}{\sqrt{2}}=10 \sqrt{2} \mathrm{A} \] Also, \(\quad \omega=100 \pi\) \(\Rightarrow \quad 2 \pi f=100 \pi\) or…
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