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(B) The brightness of the lamp depends on the current flowing through the circuit. In an $RC$ series circuit,the capacitive reactance is given by $X_{

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The lamp shines less brightly

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(B) The brightness of the lamp depends on the current flowing through the circuit. In an $RC$ series circuit,the capacitive reactance is given by $X_{C} = \frac{1}{\omega C}$. When the capacitance $C$ is reduced,the capacitive reactance $X_{C}$ increases. The total impedance of the circuit is $Z = \sqrt{R^2 + X_{C}^2}$. As $X_{C}$ increases,the total impedance $Z$ of the circuit increases. According to Ohm's law for $AC$ circuits,the current $I = \frac{V}{Z}$. Since $Z$ increases,the current $I$ flowing through the lamp decreases. Therefore,the lamp shines less brightly.

$A$ lamp is connected in series with a capacitor and an $AC$ source. What happens if the capacitance of the capacitor is reduced?

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