Question

In the circuit given below, a $100 \, W$ bulb $B_{1}$ and two $60 \, W$ bulbs $B_{2}$ and $B_{3}$ , are connected to a $250 \, V$ direct current source. If $W_{1}$ , $W_{2}$ and $W_{3}$ are the powers of the three bulbs then, which of the following statements is corect?

• A. W₁ > W₂ = W₃
• B. W₁ > W₂ > W₃
• C. W₁ < W₂ = W₃
• D. W₁ < W₂ < W₃

Answer 1

Answer: (D)

$\textit{P} = \frac{\textit{V}^{2}}{\textit{R}}$ so, $\textit{R} = \frac{\textit{V}^{2}}{\textit{P}}$
$\therefore $ $\textit{R}_{1} = \frac{\textit{V}^{2}}{\text{100}}$ and $\textit{R}_{2} = \textit{R}_{3} = \frac{\textit{V}^{2}}{\text{60}}$
Now, $\left(\textit{W}\right)_{1} = \frac{\left(\text{250}\right)^{2}}{\left(\left(\textit{R}\right)_{1} + \left(\textit{R}\right)_{2}\right)^{2}} \cdot \left(\textit{R}\right)_{1}$
$\left(\textit{W}\right)_{2} = \frac{\left(\text{250}\right)^{2}}{\left(\left(\textit{R}\right)_{1} + \left(\textit{R}\right)_{2}\right)^{2}} \cdot \left(\textit{R}\right)_{2}$ and $\left(\textit{W}\right)_{3} = \frac{\left(\text{250}\right)^{2}}{\left(\textit{R}\right)_{3}}$
W₁ : W₂ : W₃ = 15 : 25 : 64
or W₁ < W₂ < W₃ .