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  • An alternating voltage <img alt="\mathrm{V}=200 \sqrt{2} \sin (100 \mathrm{t}) \mathrm{V}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BV%7D%3D200%20%5Csqrt%7B2%7D%20%5Csin

An alternating voltage \mathrm{V}=200 \sqrt{2} \sin (100 \mathrm{t}) \mathrm{V} is connected to a  \mathrm{1 \mu \mathrm{F}} capacitor through an ac ammeter. The reading of ammeter is:

Option: 1

10 Ma


Option: 2

20 mA


Option: 3

40 mA


Option: 4

80 mA


Answers (1)

best_answer

\mathrm{Comparing \mathrm{V}=200 \sqrt{2} \sin (100 \mathrm{t}) with \mathrm{V}=\mathrm{V}_0 \sin \omega \mathrm{t}, we get \mathrm{V}=200 \sqrt{2} and \omega=100 }\mathrm{\mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{100 \times 1 \times 10^{-6}}=10^4 \Omega }
As ac instruments read rms value, the reading of ammeter is
\mathrm{\begin{aligned} & I_{\mathrm{rms}}=\frac{\mathrm{V}_{\mathrm{rms}}}{\mathrm{X}_{\mathrm{C}}}=\frac{\mathrm{V}_0}{\sqrt{2} \mathrm{X}_{\mathrm{C}}} \quad\left(\because \mathrm{V}_{\mathrm{rms}}=\frac{\mathrm{V}_0}{\sqrt{2}}\right) \\ & =\frac{200 \sqrt{2}}{\sqrt{2} \times 10^4}=2 \times 10^{-2} \mathrm{~A}=20 \mathrm{~mA} \end{aligned} }

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Ritika Harsh

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