An alternating voltage `V =200sqrt2 sin 100 t` where V is in volt and t in sec is connected to a series combination of `imuF` capacitor and `10Omega` resistor throught an ac ammeter The reading of the ammeter will be .

Options

A. `sqrt2 mA`
B. `10sqrt2mA`
C. `2mA`
D. `20mA`

Explanation

To solve the problem, we need to find the reading of the ammeter when an alternating voltage is connected to a series combination of a capacitor and a resistor. Let's break this down step by step.

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

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

### Step 3: Calculate the capacitive reactance
The capacitive reactance \( X_C \) is given by the formula:
\[ X_C = \frac{1}{\omega C} \]
Where:
- \( C = 1 \, \mu F = 1 \times 10^{-6} \, F \)
- \( \omega = 100 \, \text{rad/s} \)

Substituting the values:
\[ X_C = \frac{1}{100 \times 1 \times 10^{-6}} = \frac{1}{0.0001} = 10000 \, \Omega \]

### Step 4: Calculate the impedance of the circuit
The total impedance \( Z \) in a series circuit with a resistor \( R \) and a capacitor \( X_C \) is given by:
\[ Z = \sqrt{R^2 + X_C^2} \]
Where:
- \( R = 10 \, \Omega \)
- \( X_C = 10000 \, \Omega \)

Calculating \( Z \):
\[ Z = \sqrt{10^2 + 10000^2} = \sqrt{100 + 100000000} = \sqrt{100000100} \approx 10000 \, \Omega \]

### Step 5: Calculate the RMS current
The RMS current \( I_{\text{rms}} \) can be calculated using the formula:
\[ I_{\text{rms}} = \frac{V_{\text{rms}}}{Z} \]
Substituting the values:
\[ I_{\text{rms}} = \frac{200}{10000} = 0.02 \, \text{A} = 20 \, \text{mA} \]

### Step 6: Conclusion
The reading of the ammeter, which measures the RMS current, is:
\[ \text{Ammeter reading} = 20 \, \text{mA} \]