Two 220 volt, 100 watt bulbs are connected first in series and then in parallel. Each time combination is connected to a 220 volt a.c. supply line. The power drawn by the combination in each case respectively will be:

• A

  50 watt, 10 watt
• B

  100 watt, 50 watt
• C

  200 watt, 150 watt
• Correct answer
  D

  50 watt, 200 watt

Solution

\(\begin{aligned} & \mathrm{R}_1=\frac{\mathrm{V}^2}{\mathrm{P}_1}=\frac{(220)^2}{100}=484 \Omega \\ & \mathrm{R}_2=\frac{\mathrm{V}^2}{\mathrm{P}_2}=\frac{(220)^2}{100}=484 \Omega \\ & \mathrm{I}=\frac{220}{484 \times 2}=\frac{5}{22} \\ & \mathrm{P}=\mathrm{I}^2\left(\mathrm{R}_1+\mathrm{R}_2\right)=\frac{25}{22 \times 22} \times(484 \times 2) \\ & =50 \mathrm{~W}\end{aligned}\) \(\begin{aligned} & P=\frac{V^2}{R_1}+\frac{V^2}{R_2} \\ & =\frac{2 \times(220)^2}{484}=200 \mathrm{~W}\end{aligned}\)

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