Concept:

In a series RLC circuit, AC voltages must be added vectorially (as phasors) rather than algebraically because of the phase differences between them.

Formula:

The total source voltage \( V \) is:

$$V = \sqrt{V_R^2 + (V_L - V_C)^2}$$

Solution:

Given information:

• \( V_R = 5\text{ V} \)
• \( V_L = 10\text{ V} \)
• \( V_C = 10\text{ V} \)

At the resonance condition, the inductive reactance matches the capacitive reactance, which means the voltages across them are equal and in exact phase opposition (\( 180^\circ \) out of phase):

$$V = \sqrt{5^2 + (10 - 10)^2} = \sqrt{5^2 + 0} = 5\text{ V}$$

The total applied voltage is simply equal to the voltage drop across the resistor.

Why other options are incorrect:

• 20 V and 25 V result from simple algebraic addition (e.g., \( 5 + 10 + 10 = 25\text{ V} \)), which completely ignores phase vector alignment.



• 10 V is the value of the reactive components alone.