A circuit element $X$ when connected to an AC supply of peak voltage $100 \mathrm{V}$ gives a peak current of $5 \mathrm{A}$ which is in phase with the voltage. A second element $Y$ when connected to the same AC supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi }{2}$. If $X$ and $Y$ are connected in series to the same supply, what will be the rms value of the current in ampere?

• A

  $\frac{10}{\sqrt{2}}$
• B

  $\frac{5}{\sqrt{2}}$
• C

  $5\sqrt{2}$
• Correct answer
  D

  $\frac{5}{2}$

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