An electric bulb and a capacitor are connected in series with an `AC` source.On increasing the freqency of the source, the brightness of the bulb

Options

A. increase
B. decrease
C. remains uncharged
D. sometime increases and sometimes decreases

Answer

To solve the problem step by step, we need to analyze the situation where an electric bulb and a capacitor are connected in series with an AC source, and we want to understand how the brightness of the bulb changes when the frequency of the AC source is increased.

### Step 1: Understand the Components
- **Electric Bulb**: The brightness of the bulb depends on the current flowing through it. More current means more brightness.
- **Capacitor**: In an AC circuit, a capacitor has a property called capacitive reactance (Xc), which opposes the flow of current.

### Step 2: Relationship Between Capacitive Reactance and Frequency
- The capacitive reactance (Xc) is given by the formula:
\[ X_c = \frac{1}{2\pi f C} \]
where:
- \( X_c \) is the capacitive reactance,
- \( f \) is the frequency of the AC source,
- \( C \) is the capacitance of the capacitor.

### Step 3: Analyze the Effect of Increasing Frequency
- From the formula, we can see that \( X_c \) is inversely proportional to the frequency \( f \). This means that as the frequency increases, the capacitive reactance \( X_c \) decreases.
- Mathematically, if \( f \) increases, then \( X_c \) decreases.

### Step 4: Impact on Current and Brightness
- Since the bulb and capacitor are in series, the total impedance (Z) of the circuit will also change. The total impedance in a series circuit with a capacitor is affected by the capacitive reactance.
- As \( X_c \) decreases, the total impedance \( Z \) of the circuit decreases, leading to an increase in the current \( I \) flowing through the circuit.
- The current through the bulb is what determines its brightness. Therefore, as the current increases, the brightness of the bulb also increases.

### Step 5: Conclusion
- Thus, when the frequency of the AC source is increased, the brightness of the bulb increases.

### Final Answer
- The brightness of the bulb will **increase** when the frequency of the AC source is increased.

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