Question

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

• A. 13 V
• B. 17 V
• C. 5 V
• D. 12 V

Hint:

Do not just add AC voltages; use the Pythagorean theorem for series components.

Answer 1

The Correct Option is A

Step 1: Phasor Concept
In a series RC circuit, the voltages across the resistor ($V_R$) and capacitor ($V_C$) are $90^{\circ}$ out of phase.
Step 2: Vector Sum
Total voltage $V = \sqrt{V_R^2 + V_C^2}$.
Step 3: Calculation
$V = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$ V.
Final Answer: (a)