A lamp is connected in series with a capacitor and connected to an AC source. As the capacitance value is decreased.a)The lamp glows dimmer and dimmerb)The lamp does not glowc)The lamp glows brighterd)The lamp starts turning on and offCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

When frequency decreases, capacitive reactance XC=1/2πνC increases and hence impedance in the circuit Z=√(R2+XC2) increases and so current I=V/Z decreases. As a result, the brightness of the bulb is reduced.

Answer

We know capacitive reactant= 1/wC
where 'w' is angular frequency and if we decrease The capacitance then reactant increase and so net resistance of the circuit increases hence current decrease and so voltage across lamp decrease and the lamp glows dimmer and dimmer

Answer

The correct answer is option 'A': The lamp glows dimmer and dimmer.

Explanation:
When a lamp is connected in series with a capacitor and connected to an AC source, the behavior of the lamp depends on the value of the capacitor.

1. Capacitors in AC circuits:
In an AC circuit, capacitors act as reactive components. They store and release electrical energy in response to changes in voltage. Capacitors have a property called reactance (Xc), which is the opposition to the flow of AC current. The reactance of a capacitor depends on its capacitance value and the frequency of the AC source.

2. Effect of decreasing capacitance:
As the capacitance value is decreased in the given circuit, the reactance of the capacitor increases. This means that the capacitor becomes a stronger opposition to the flow of AC current.

3. Voltage drop across the lamp:
In a series circuit, the total voltage across the components is equal to the sum of the individual voltage drops. As the reactance of the capacitor increases, more voltage is dropped across it. Consequently, the voltage across the lamp decreases.

4. Relationship between voltage and brightness:
The brightness of a lamp is directly proportional to the voltage across it. As the voltage across the lamp decreases due to the increasing reactance of the capacitor, the lamp glows dimmer and dimmer. This is because the lower voltage leads to a lower current flowing through the lamp, resulting in reduced brightness.

5. The lamp does not turn off completely:
Although the lamp glows dimmer, it does not turn off completely. This is because even with a smaller capacitance, there is still some voltage drop across the capacitor. Therefore, there is still some current flowing through the lamp, causing it to emit a faint glow.

In summary, when the capacitance value is decreased in a series circuit with a lamp and a capacitor connected to an AC source, the lamp glows dimmer and dimmer due to the increased reactance of the capacitor, which leads to a reduced voltage across the lamp.

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