What will happen when a 40 watt-220 volt lamp and a 100 watt-220 volt lamp are connected in series across 40 volt supply?

Bulb (I): Rated current $I_{1} = \frac{P}{V} = \frac{40}{220} = \frac{2}{11} A$

Resistance, $R_{1} = \frac{V^{2}}{P} = \frac{{(220)}^{2}}{40} = 1210 Ω$

Bulb (II) : Rated current, $I_{2} = \frac{100}{220} = \frac{5}{11} A$

Resistance, $R_{2} = \frac{{(220)}^{2}}{100} = 484 Ω$

When both are connected in series across 40 V supply

Total current through supply

$R_{1} = \frac{40}{R_{1} + R_{2}} = \frac{40}{1210 + 484} = \frac{40}{1694} = 0 .023 A$

This current is less than the rated current of each bulb. So neither bulb will fuse.

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