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`

Answer

To solve the problem step by step, we need to find the RMS current reading on the ammeter when an alternating voltage is applied to a capacitor.

### Step 1: Identify the given values
The given alternating voltage is:
\[ E(t) = 200\sqrt{2} \sin(100t) \]
From this, we can identify:
- \( V_0 = 200\sqrt{2} \) (the peak voltage)
- The angular frequency \( \omega = 100 \, \text{rad/s} \)

The capacitance \( C \) is given as:
\[ C = 1 \, \mu F = 1 \times 10^{-6} \, F \]

### Step 2: Calculate the RMS voltage
The RMS voltage \( V_{rms} \) can be calculated using the formula:
\[ V_{rms} = \frac{V_0}{\sqrt{2}} \]
Substituting the value of \( V_0 \):
\[ V_{rms} = \frac{200\sqrt{2}}{\sqrt{2}} = 200 \, V \]

### Step 3: Calculate the capacitive reactance \( X_C \)
The capacitive reactance \( X_C \) is given by the formula:
\[ X_C = \frac{1}{\omega C} \]
Substituting the values of \( \omega \) and \( C \):
\[ X_C = \frac{1}{100 \times 1 \times 10^{-6}} = \frac{1}{0.0001} = 10000 \, \Omega \]

### Step 4: Calculate the RMS current \( I_{rms} \)
The RMS current \( I_{rms} \) can be calculated using Ohm's law for AC circuits:
\[ I_{rms} = \frac{V_{rms}}{X_C} \]
Substituting the values we calculated:
\[ I_{rms} = \frac{200}{10000} = 0.02 \, A = 20 \, mA \]

### Final Answer
The reading of the ammeter shall be:
\[ \boxed{20 \, mA} \]

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