Question

In the circuit given below, a $100W$ bulb $B_1$ and two $60W$ bulbs $B_2$ and $B_3$ , are connected to a $250V$ 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)

$\text{P}=\frac{{\text{V}}^2}{\text{R}}$ so, $\text{R}=\frac{{\text{V}}^2}{\text{P}}$
$\therefore$ ${\text{R}}_1=\frac{{\text{V}}^2}{\text{100}}$ and ${\text{R}}_2={\text{R}}_3=\frac{{\text{V}}^2}{\text{60}}$
Now, ${\left(\text{W}\right)}_1=\frac{{\left(\text{250}\right)}^2}{{\left({\left(\text{R}\right)}_1+{\left(\text{R}\right)}_2\right)}^2}\cdot {\left(\text{R}\right)}_1$
${\left(\text{W}\right)}_2=\frac{{\left(\text{250}\right)}^2}{{\left({\left(\text{R}\right)}_1+{\left(\text{R}\right)}_2\right)}^2}\cdot {\left(\text{R}\right)}_2$ and ${\left(\text{W}\right)}_3=\frac{{\left(\text{250}\right)}^2}{{\left(\text{R}\right)}_3}$
W₁ : W₂ : W₃ = 15 : 25 : 64
or W₁ < W₂ < W₃ .