A bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased, while keeping the voltage of the source constant, then

Options

A. Bulb will give more intense light
B. Bulb will give less intense light
C. Bulb will give light of same intensity as before
D. Bulb will stop radiating light

Explanation

To solve the problem step by step, let's analyze the situation where a bulb and a capacitor are connected in series to an alternating current (AC) source, and we are increasing the frequency of the AC source while keeping the voltage constant.

### Step 1: Understand the Circuit
We have a circuit consisting of:
- A bulb (which acts as a resistor)
- A capacitor
- An AC voltage source

### Step 2: Identify the Impedance
The total impedance (Z) of the circuit can be calculated using the formula:
\[ Z = \sqrt{R^2 + X_C^2} \]
where:
- \( R \) is the resistance of the bulb
- \( X_C \) is the capacitive reactance

### Step 3: Calculate Capacitive Reactance
The capacitive reactance (\( X_C \)) is given by:
\[ X_C = \frac{1}{2 \pi f C} \]
where:
- \( f \) is the frequency of the AC source
- \( C \) is the capacitance of the capacitor

### Step 4: Effect of Increasing Frequency
When the frequency (\( f \)) is increased:
- The value of \( X_C \) decreases because it is inversely proportional to frequency.
- Therefore, as \( f \) increases, \( X_C \) decreases.

### Step 5: Calculate New Impedance
With \( X_C \) decreasing, the total impedance \( Z \) will also decrease:
\[ Z = \sqrt{R^2 + X_C^2} \]
Since \( X_C \) is decreasing, the overall impedance \( Z \) decreases.

### Step 6: Analyze Current Flow
Using Ohm's Law, the current (\( I \)) in the circuit can be calculated as:
\[ I = \frac{V}{Z} \]
where \( V \) is the voltage of the AC source.

Since the voltage \( V \) is kept constant and the impedance \( Z \) has decreased, the current \( I \) must increase:
- \( I \) increases as \( Z \) decreases.

### Step 7: Effect on Bulb Brightness
The brightness of the bulb is directly related to the current flowing through it. An increase in current means:
- The bulb will glow more brightly.

### Conclusion
Thus, when the frequency of the AC source is increased while keeping the voltage constant, the bulb will glow more intensely.

### Final Answer
The correct answer is: The bulb will give more intense light.

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