SATHEE: Current Electricity 3 Question 10

Current Electricity 3 Question 10

9. A $100 W$ bulb $B_{1}$ , and two $60 W$ bulbs $B_{2}$ and $B_{3}$ , are connected to a $250 V$ source, as shown in the figure. Now $W_{1}, W_{2}$ and $W_{3}$ are the output powers of the bulbs $B_{1}, B_{2}$ and $B_{3}$ respectively. Then,

(2002, 2M)

(a) $W_{1} > W_{2} = W_{3}$

(b) $W_{1} > W_{2} > W_{3}$

(d) $W_{1} < W_{2} < W_{3}$

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Solution:

$P = \frac{V^{2}}{R}$ so, $R = \frac{V^{2}}{P}$

$∴ R_{1} = \frac{V^{2}}{100} and R_{2} = R_{3} = \frac{V^{2}}{60}$

$Now, W_{1} = \frac{(250)^{2}}{{(R_{1} + R_{2})}^{2}} \cdot R_{1}$

$\begin{matrix} W_{2} = \frac{(250)^{2}}{{(R_{1} + R_{2})}^{2}} \cdot R_{2} and W_{3} = \frac{(250)^{2}}{R_{3}} \\ W_{1} : W_{2} : W_{3} = 15 : 25 : 64 or W_{1} < W_{2} < W_{3} \end{matrix}$

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Current Electricity 3 Question 10

9. A 100W bulb B1, and two 60W bulbs B2 and B3, are connected to a 250V source, as shown in the figure. Now W1,W2 and W3 are the output powers of the bulbs B1,B2 and B3 respectively. Then,

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9. A $100 W$ bulb $B_{1}$ , and two $60 W$ bulbs $B_{2}$ and $B_{3}$ , are connected to a $250 V$ source, as shown in the figure. Now $W_{1}, W_{2}$ and $W_{3}$ are the output powers of the bulbs $B_{1}, B_{2}$ and $B_{3}$ respectively. Then,