\(\mathrm{R}=\frac{\mathrm{V}^2}{\mathrm{P}}=\frac{(200)^2}{50}=\frac{40000}{50}\)

\(\mathrm{R}=800\)

\(\mathrm{P}=\frac{\left(\mathrm{V}_{\text {applied }}\right)^2}{\mathrm{R}}=\frac{(100)^2}{800}\)

\(\mathrm{P}=12.5 \text { watt }\)

Hence option \(1\) is correct.