Question

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?

• A. 100 watt lamp will fuse
• B. 40 watt lamp will fuse
• C. Both lamps will fuse
• D. Neither lamp will fuse

Answer 1

Answer: (D)

Bulb (I): Rated current $I_1=\frac{P}{V}$
$=\frac{40}{220}=\frac{2}{11}A$
Resistance, $R_1=\frac{V^2}{P}$
$=\frac{(220{)}^2}{40}=1210\Omega$
Bulb (II): Rated current, $I_2=\frac{100}{220}$
$=\frac{5}{11}A$
Resistance, $R_2=\frac{(220{)}^2}{100}=484\Omega$
When both are connected in series across $40V$ supply

Total current through supply
$R_1=\frac{40}{R_1+R_2}=\frac{40}{1210+484}$
$=\frac{40}{1694}=0.023A$
This current is less than the rated current of each bulb. So neither bulb will fuse.