Question

If bulb-$1$ of $25W$ and bulb$-2$ of $100W$ rated at $220V$ are connected in series across a $440V$ supply, will both the bulbs fuse? If not which one?

Answer 1

As for an electric appliance, $R=V_s^2/W$, so for same specified voltage $V_s$,

$\frac{R_{25}}{R_{100}}=\frac{100}{25}=4$ i.e., $R_{25}=4R$ with $R_{100}=R$

Now, in series, potential divides in proportion to resistance. So,

$V_1=\frac{R_1}{(R_1+R_2)}V$, i.e., $V_{25}=\frac{4}{5}\times 440=352V$

$V_2=\frac{R_1}{(R_1+R_2)}V$, i.e., $V_{100}=\frac{1}{5}\times 440=88V$

From this, it is clear that voltage across the $100W$ bulb $(=88V)$ is lesser than specified $\left(220V\right),$ while across the 25 W bulb (= 352 V) is greater than specified $\left(220V\right),$ so the $25W$ bulb will fuse.