MHT CET · Physics · Alternating Current
The a.c. source of e.m.f. with instantaneous value ' \(e\) ' is given by \(e=200 \sin (50 t)\) volt. The r.m.s. value of current in a circuit of resistance \(50 \Omega\) is
- A \(0.2828 \mathrm{~A}\)
- B \(2.828 \mathrm{~A}\)
- C \(28.28 \mathrm{~A}\)
- D \(282.8 \mathrm{~A}\)
Answer & Solution
Correct Answer
(B) \(2.828 \mathrm{~A}\)
Step-by-step Solution
Detailed explanation
\(\therefore \quad\) e.m.f e \(=200 \sin (50 \mathrm{t}) \mathrm{V}\)
\(\therefore \quad\) Current is given by:
\(\mathrm{I}_{\mathrm{o}}=\frac{\mathrm{e}_{\mathrm{o}}}{\mathrm{R}}=\frac{200}{50}=4 \mathrm{~A}\) .....(from (i))
\(\therefore \quad\) R.M.S value of current:
\(I_{\mathrm{r} . \mathrm{ms}}=\frac{\mathrm{I}_{\circ}}{\sqrt{2}}=\frac{4}{\sqrt{2}}=2.828 \mathrm{~A}\)
\(\therefore \quad\) Current is given by:
\(\mathrm{I}_{\mathrm{o}}=\frac{\mathrm{e}_{\mathrm{o}}}{\mathrm{R}}=\frac{200}{50}=4 \mathrm{~A}\) .....(from (i))
\(\therefore \quad\) R.M.S value of current:
\(I_{\mathrm{r} . \mathrm{ms}}=\frac{\mathrm{I}_{\circ}}{\sqrt{2}}=\frac{4}{\sqrt{2}}=2.828 \mathrm{~A}\)
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