Bulb ${\mathrm{B}}_1\left(\mathrm{100 }\mathrm{W}–\mathrm{250 }\mathrm{V}\right)$ and bulb ${\mathrm{B}}_2\left(100\mathrm{ }\mathrm{W}\mathrm{ }–\mathrm{ }\mathrm{200 }\mathrm{V}\right)$ are connected across $250\mathrm{ }\mathrm{V}$. What is potential drop across ${\mathrm{B}}_2$?

• A

  $200\mathrm{ }\mathrm{V}$
• B

  $250\mathrm{ }\mathrm{V}$
• Correct answer
  C

  $98\mathrm{ }\mathrm{V}$
• D

  $48\mathrm{ }\mathrm{V}$

Solution

Resistance of bulb ${\mathrm{B}}_1,\mathrm{ }{\mathrm{R}}_1=\frac{{\left(250\right)}^2}{100}=\mathrm{ }625\mathrm{ }\mathrm{\Omega }$

Resistance of bulb ${\mathrm{B}}_2,\mathrm{ }{\mathrm{R}}_2=\frac{{\left(200\right)}^2}{100}=\mathrm{ }400\mathrm{ }\mathrm{\Omega }$



${\mathrm{V}}_{{\mathrm{R}}_2}=\mathrm{ }\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1+{\mathrm{R}}_2}\times \mathrm{ }250=\frac{400}{625+400}\times \mathrm{ }250=\mathrm{98 }\mathrm{V}$

Hence, the correct answer is option: 'C'.