Mathematics

When bulbs are in series, they share the voltage—each gets only 3 V instead of the full 6 V. Since the power dissipated in a bulb depends on $P = \frac{V^2}{R}$, cutting the voltage in half reduces the power to one-quarter, making each bulb glow much dimmer. The key insight is that voltage divides across series resistances, so adding more bulbs in series starves each one of the energy it needs to shine brightly.

When bulbs are in series, they share the voltage—each gets only 3 V instead of the full 6 V. Since the power dissipated in a bulb depends on $P = \frac{V^2}{R}$, cutting the voltage in half reduces the power to one-quarter, making each bulb glow much dimmer. The key insight is that voltage divides across series resistances, so adding more bulbs in series starves each one of the energy it needs to shine brightly.