Two electric bulbs marked $25 \mathrm{~W}-220 \mathrm{~V}$ and $100 \mathrm{~W}-220 \mathrm{~V}$ are…
Two electric bulbs marked $25 \mathrm{~W}-220 \mathrm{~V}$ and $100 \mathrm{~W}-220 \mathrm{~V}$ are connected in series to a $440 \mathrm{~V}$ supply.
Which of the bulbs will fuse?
both
$100 \mathrm{~W}$
$25 \mathrm{~W}$
neither
Solution
Resistances of both the bulbs are
$\mathrm{R}_1=\frac{\mathrm{V}^2}{\mathrm{P}_1}=\frac{220^2}{25}$
$\mathrm{R}_2=\frac{\mathrm{V}^2}{\mathrm{P}_2}=\frac{220^2}{100}$
Hence $R_1>R_2$
When connected in series, the voltages divide in them in the ratio of their resistances. The voltage of $440\mathrm{~V}$ devides in such a way that voltage across $25 \mathrm{~w}$ bulb will be more than $220 \mathrm{~V}$.
Hence $25 \mathrm{~w}$ bulb will fuse.