Step 1: Understanding the Concept:
An AC ammeter measures the root mean square (rms) value of the current flowing through the circuit.
In a purely capacitive circuit, the current depends on the rms voltage and the capacitive reactance. Step 2: Key Formula or Approach:
Voltage equation: \(V = V_0 \sin(\omega t)\). Here \(V_0 = 100\sqrt{2}\text{ V}\), \(\omega = 50\text{ rad/s}\).
RMS voltage: \(V_{\text{rms}} = V_0 / \sqrt{2}\).
Capacitive reactance: \(X_C = \frac{1}{\omega C}\).
Ohm's Law for AC: \(I_{\text{rms}} = \frac{V_{\text{rms}}}{X_C} = V_{\text{rms}} \cdot \omega C\). Step 3: Detailed Explanation:
Calculate RMS voltage:
\[ V_{\text{rms}} = \frac{100\sqrt{2}}{\sqrt{2}} = 100\text{ V} \]
Calculate current \(I_{\text{rms}}\):
\[ I_{\text{rms}} = 100 \times 50 \times (2 \times 10^{-6}) \]
\[ I_{\text{rms}} = 100 \times 100 \times 10^{-6} \]
\[ I_{\text{rms}} = 10^4 \times 10^{-6} = 10^{-2}\text{ A} \]
Convert Amperes to milliamperes:
\[ I_{\text{rms}} = 0.01 \text{ A} = 10\text{ mA} \]
Step 4: Final Answer:
The ammeter reading will be \(10\text{ mA}\).