Question 343: AC fundamentals

Question

An alternating voltage $\mathrm{v}=200 \sqrt{2} \sin (100 \mathrm{t})$ is connected to a $1 \mu \mathrm{~F}$ capacitor through an a. c. ammeter. The reading of the ammeter shall be

Accepted Answer

Alternating voltage: $e=200 \sqrt{2} \sin (100 t)$ volt
Comparing with $\mathrm{e}=\mathrm{e}_0 \sin \omega t$
$$\omega=100 \mathrm{rad} / \mathrm{s}, e_0=200 \sqrt{2}$$
Capacitive reactance,
$$\begin{aligned}
& \mathrm{X}_{\mathrm{C}}=\frac{1}{\omega \mathrm{C}}=\frac{1}{100 	imes 10^{-6}} \Omega=10^4 \Omega \
& \mathrm{I}_0=\frac{\mathrm{e}_0}{\mathrm{X}_{\mathrm{c}}} \
& \mathrm{I}_0=\frac{200 \sqrt{2}}{10^4} \
& \mathrm{I}_0=2 \sqrt{2} 	imes 10^{-2} \mathrm{~A} \
& \mathrm{I}_{\mathrm{rms}}=\frac{\mathrm{I}_0}{\sqrt{2}}=\frac{2 \sqrt{2} 	imes 10^{-2}}{\sqrt{2}}=2 	imes 10^{-2} \mathrm{~A}=20 \mathrm{~mA}
\end{aligned}$$

Answer

10 mA

Answer

20 mA

Answer

40 mA

Answer

80 mA

AC fundamentals

An alternating voltage \mathrm{v}=200 \sqrt{2} \sin (100 \mathrm{t}) is connected to a 1 \mu \mathrm{~F} capacitor through an a. c. ammeter. The reading of the ammeter shall be

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