Concept:The brightness of the bulb depends on the current flowing through it, which is controlled by the capacitive reactance of the capacitor in the AC circuit.
Explanation:For a capacitor connected to an AC source, the capacitive reactance is given by:
XC​=2πfC1​where
f is the frequency of the AC source and
C is the capacitance.
The bulb and capacitor are in series, so the same current flows through both.
If
XC​ increases, the impedance of the circuit increases, and the current decreases.
A smaller current means the bulb glows with reduced brightness.
When the capacitance
C is reduced, the denominator
2Ï€fC becomes smaller, so
XC​ increases.
Hence, the current decreases and the brightness of the bulb is reduced.
When the frequency
f is reduced, the product
2Ï€fC also becomes smaller, so
XC​ increases again.
Thus, the current decreases and the brightness of the bulb is reduced in this case as well.
Therefore, reducing capacitance and reducing frequency both cause the brightness to be reduced.
Answer:Option A: is reduced, is reduced