First slide

Electrical power

Question

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

Moderate

A

W₁ > W₂ = W₃
B

W₁ > W₂ > W₃
C

W₁ < W₂ = W₃
D

W₁ < W₂ < W₃

Solution

$P = \frac{V^{2}}{R} so R = \frac{V^{2}}{P} \Rightarrow R_{1} = \frac{V^{2}}{100} and R_{2} = R_{3} = \frac{V^{2}}{60}$
$\begin{array}{l} Now W_{1} = \frac{{(250)}^{2}}{{(R_{1} + R_{2})}^{2}} . R_{1}, W_{2} = \frac{{(250)}^{2}}{{(R_{1} + R_{2})}^{2}} . R_{2} \\ and W_{3} = \frac{{(250)}^{2}}{R_{3}} \end{array}$
W₁ : W₂ : W₃ = 15 : 25 : 64 or W₁ < W₂ < W₃

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