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:

  1. (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.