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AIEEE 2012 Solved Paper

Section: Physics

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Question : 46 of 89

Marks: +1, -0

Two electric bulbs marked

25 \text{W}-220 \text{V}

100 \text{W}-220 \text{V}

are connected in series to a

440 \text{V}

supply. Which of the bulbs will fuse?

Both
$100 \text{W}$
$25 \text{W}$
Neither

Solution:

The current upto which bulb of marked

25 \text{W}-220 \text{V}

, will not fuse

I_1=\;\frac{W_1}{V_1}=\;\frac{25}{220} \text{Amp}

Similarly,

I_2=\;\frac{W_2}{V_2}=\;\frac{100}{220} \text{Amp}

The current flowing through the circuit

I=\;\frac{440}{R_{\text{eff}}},\; R_{\text{eff}}=R_1+R_2

R_1=\;\frac{V_1^2}{P_1}=\;\frac{(220)^2}{25}

R_2=\;\frac{V_2^2}{P}=\;\frac{(220)^2}{100}

I=\;\frac{440}{\frac{(220)^2}{25}+\;\frac{(220)^2}{100}}

=\;\frac{440}{(220)^2 \left[\frac{1}{25}+\;\frac{1}{100}\right]}

I=\;\frac{40}{220} \text{Amp}

\;\;\text{ as }\; I_1 \left(=\;\frac{25}{220} \text{A}\right) < I \left(=\;\frac{40}{220} \text{A}\right) < I_2 \left(=\;\frac{100}{200} \text{A}\right)

Thus the bulb marked

25 \text{W}-220

will fuse.

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