An alternating voltage `E=200sqrt(2)sin(100t)` is connected to a `1` microfarad capacitor through an AC ammeter. The reading of the ammeter shall be

Options

A. 10 mA
B. 20 mA
C. 40 mA
D. 80 mA

Explanation

To solve the problem, we need to find the reading of the AC ammeter when an alternating voltage is applied to a capacitor. Here’s the step-by-step solution:

### Step 1: Identify the given parameters
The alternating voltage is given by:
\[ E(t) = 200\sqrt{2} \sin(100t) \]
The capacitance of the capacitor is:
\[ C = 1 \, \mu F = 1 \times 10^{-6} \, F \]

### Step 2: Determine the angular frequency (ω)
From the voltage equation, we can identify the angular frequency:
\[ \omega = 100 \, \text{rad/s} \]

### Step 3: Calculate the capacitive reactance (XC)
The capacitive reactance \( X_C \) is given by the formula:
\[ X_C = \frac{1}{\omega C} \]
Substituting the values:
\[ X_C = \frac{1}{100 \times 1 \times 10^{-6}} \]
\[ X_C = \frac{1}{100 \times 10^{-6}} = 10^4 \, \Omega = 10000 \, \Omega \]

### Step 4: Calculate the RMS voltage (ERMS)
The peak voltage \( E_0 \) is given as \( 200\sqrt{2} \). The RMS voltage \( E_{RMS} \) can be calculated using:
\[ E_{RMS} = \frac{E_0}{\sqrt{2}} \]
Substituting the value:
\[ E_{RMS} = \frac{200\sqrt{2}}{\sqrt{2}} = 200 \, V \]

### Step 5: Calculate the RMS current (IRMS)
The RMS current \( I_{RMS} \) can be calculated using Ohm's law for AC circuits:
\[ I_{RMS} = \frac{E_{RMS}}{X_C} \]
Substituting the values:
\[ I_{RMS} = \frac{200}{10^4} = \frac{200}{10000} = 0.02 \, A \]
Converting to milliampere:
\[ I_{RMS} = 20 \, mA \]

### Step 6: Conclusion
The reading of the ammeter will be:
\[ \text{Ammeter reading} = 20 \, mA \]