MHT CET · Physics · Alternating Current
An alternating voltage \(E=200 \sqrt{2} \sin (100 t)\) volt is connected to a \(1 \mu \mathrm{f}\) capacitor through an a.c. ammeter. The reading of the ammeter shall
- A \(10 \mathrm{~mA}\)
- B \(20 \mathrm{~mA}\)
- C \(40 \mathrm{~mA}\)
- D \(80 \mathrm{~Ma}\)
Answer & Solution
Correct Answer
(B) \(20 \mathrm{~mA}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{V}_{\mathrm{rms}}=\frac{\mathrm{I}_{\mathrm{rms}}}{\mathrm{X}_{\mathrm{C}}} \)
\( \therefore \mathrm{I}_{\mathrm{ms}} =\frac{\mathrm{V}_{\mathrm{o}} \omega \mathrm{C}}{\sqrt{2}}=\frac{200 \sqrt{2} \times 100 \times 1 \times 10^{-6}}{\sqrt{2}}\) \(=20 \mathrm{~mA}\)
\( \therefore \mathrm{I}_{\mathrm{ms}} =\frac{\mathrm{V}_{\mathrm{o}} \omega \mathrm{C}}{\sqrt{2}}=\frac{200 \sqrt{2} \times 100 \times 1 \times 10^{-6}}{\sqrt{2}}\) \(=20 \mathrm{~mA}\)
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