Current Electricity - Result Question 78
83. If $25 W, 220 V$ and $100 W, 220 V$ bulbs are connected in series across a $440 V$ line, then
[2001]
(a) only $25 W$ bulb will fuse
(b) only $100 W$ bulb will fuse
(c) both bulbs will fuse
(d) none of these
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Answer:
Correct Answer: 83. (a)
Solution:
- (a) 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, $R _{25}=4 R$ 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., $V _{25}=\frac{4}{5} \times 440=352 V$
and $V_2=\frac{R_2}{(R_1+R_2)} V$
i.e., $V _{100}=\frac{1}{5} \times 440=88 V$
From this, it is clear that voltage across $100 W$ bulb $(=88 V)$ is lesser than specified $(220 V)$ while across $25 W$ bulb $(=352 V)$ is greater than specified $(220 V)$, so, $25 W$ bulb will fuse.
