A lamp is connected in series with a capacitor. Predict your observations for dc and ac connections. What happens in each case if the capacitance of the capacitor is reduced?
For DC connection: When a DC source is connected, the capacitor gets charged initially. After charging is complete, no current flows in the circuit, so the lamp will not glow. Even if the capacitance is reduced, there will be no change in this observation.
For AC connection: When an AC source is connected, the capacitor offers capacitive reactance (), allowing current to flow in the circuit. Hence, the lamp will glow. If the capacitance is reduced, the capacitive reactance increases (since ), which reduces the current flow. As a result, the lamp will shine less brightly than before.
Explanation
The textbook solution clearly distinguishes between DC and AC behavior of a capacitor. In DC, the capacitor charges once and then blocks current completely. In AC, the capacitor offers reactance and allows continuous current flow. The relationship shows that reducing capacitance increases reactance, thereby reducing current and brightness.