Two lamps 100 W and 40 W are connected in series across 230 V (alternating). Which of the following statement is correct?

The correct answer is: D. 40 W lamp will fuse.

When two lamps of different wattages are connected in series, the current through each lamp will be the same. However, the voltage drop across each lamp will be proportional to its wattage. In this case, the 100 W lamp will have a voltage drop of 100 V, while the 40 W lamp will have a voltage drop of 40 V. This means that the 100 W lamp will be under a higher current and voltage than the 40 W lamp. As a result, the 40 W lamp will overheat and fuse.

Here is a more detailed explanation of each option:

• Option A: The 100 W lamp will glow brighter. This is not correct because the current through each lamp is the same. Therefore, the 40 W lamp will also glow brightly.
• Option B: The 40 W lamp will glow brighter. This is not correct because the 100 W lamp will be under a higher current and voltage than the 40 W lamp. As a result, the 100 W lamp will glow brighter.
• Option C: Both lamps will glow equally bright. This is not correct because the current through each lamp is the same, but the voltage drop across each lamp is proportional to its wattage. In this case, the 100 W lamp will have a voltage drop of 100 V, while the 40 W lamp will have a voltage drop of 40 V. This means that the 100 W lamp will be under a higher current and voltage than the 40 W lamp. As a result, the 100 W lamp will glow brighter.
• Option D: The 40 W lamp will fuse. This is the correct answer because the 40 W lamp will be under a higher current and voltage than the 100 W lamp. As a result, the 40 W lamp will overheat and fuse.