A lamp is connected in series with a capacitor. Predict your observations for dc and ac connections. What happens in each case if capacitance of the capacitor is reduced?

Options

A. lamp will not glow
B. lamp will burst out
C. lamp will glow normally
D. None of these

Answer

To analyze the behavior of a lamp connected in series with a capacitor under DC and AC connections, we will break down the observations step by step.

### Step-by-Step Solution:

1. **Understanding the Circuit with DC Connection:**
- When a DC voltage source is connected to the circuit, the capacitor will start charging.
- The charging process continues until the capacitor reaches its maximum voltage, which is equal to the supply voltage.

**Observation:**
- Once the capacitor is fully charged, it acts like an open circuit. Therefore, the current in the circuit becomes zero.

2. **Effect on the Lamp:**
- Since the current is zero in the steady state, the lamp will not glow at all.

3. **Understanding the Circuit with AC Connection:**
- When an AC voltage source is connected, the capacitor will continuously charge and discharge due to the alternating nature of the AC voltage.
- The capacitive reactance (Xc) is given by the formula:
\[ X_c = \frac{1}{\omega C} \]
where \( \omega \) is the angular frequency of the AC source and \( C \) is the capacitance.

4. **Effect of Reducing Capacitance:**
- If the capacitance \( C \) is reduced, the capacitive reactance \( X_c \) increases.
- The total impedance \( Z \) of the circuit will also increase, which can be expressed as:
\[ Z = \sqrt{R^2 + X_c^2} \]
where \( R \) is the resistance of the lamp.

5. **Current in the Circuit:**
- The current \( I \) in the circuit can be calculated using Ohm's law:
\[ I = \frac{E}{Z} \]
where \( E \) is the voltage of the AC source.
- As \( Z \) increases due to the increase in \( X_c \), the current \( I \) decreases.

6. **Effect on the Lamp:**
- Since the current is flowing but at a reduced level, the lamp will glow, but with less brightness compared to when the capacitance was higher.

### Summary of Observations:
- **DC Connection:** The lamp does not glow because the current is zero after the capacitor is fully charged.
- **AC Connection:** The lamp glows with reduced brightness when the capacitance is decreased, as the current in the circuit decreases due to increased reactance.