A resistor and a capacitor are connected in series with an AC source. If the potential drop across the capacitor is $5 \mathrm{~V}$ and that across resistor is $12 \mathrm{~V}$, then applied voltage is

• Correct answer
  A

  $13 \mathrm{~V}$
• B

  $17 \mathrm{~V}$
• C

  $5 \mathrm{~V}$
• D

  $12 \mathrm{~V}$

Solution

Let the applied voltage be $V$ volt.

Here, $\mathrm{V}_{\mathrm{R}}=12 \mathrm{~V}, \mathrm{~V}_{\mathrm{C}}=5 \mathrm{~V}$ $$ \begin{aligned} \therefore \quad \mathrm{V} &=\sqrt{\mathrm{V}_{\mathrm{R}}^{2}+\mathrm{V}_{\mathrm{C}}^{2}}=\sqrt{(12)^{2}+(5)^{2}} \\ &=\sqrt{144+25}=\sqrt{169}=13 \mathrm{~V} \end{aligned} $$

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