In an AC circuit, an alternating voltage $\varepsilon = 200\sqrt{2}\sin(100t)$ V is connected to a capacitor o

Question

In an AC circuit, an alternating voltage $\varepsilon = 200\sqrt{2}\sin(100t)$ V is connected to a capacitor of capacity $1 \mu	ext{F}$. The RMS value of the current in the circuit is:

Accepted Answer

1.  **Identify Parameters:** Compare the given voltage equation $\varepsilon = 200\sqrt{2}\sin(100t)$ with the standard form $V = V_m \sin(\omega t)$. 
    *   Peak Voltage $V_m = 200\sqrt{2}$ V.
    *   Angular Frequency $\omega = 100$ rad/s.
    *   Capacitance $C = 1 \mu	ext{F} = 1 	imes 10^{-6}$ F.
2.  **Calculate Reactance:** The capacitive reactance is $X_C = \frac{1}{\omega C} = \frac{1}{100 	imes 10^{-6}} = \frac{1}{10^{-4}} = 10^4 \, \Omega$ .
3.  **Calculate RMS Voltage:** $V_{rms} = \frac{V_m}{\sqrt{2}} = \frac{200\sqrt{2}}{\sqrt{2}} = 200$ V .
4.  **Calculate RMS Current:** $I_{rms} = \frac{V_{rms}}{X_C} = \frac{200}{10^4} = 0.02$ A.
5.  **Convert Units:** $0.02 	ext{ A} = 20$ mA.

Step-by-Step Solution

Practice All PHYSICS Questions