Question

The value of alternating e.m.f. (\(E\)) in the given circuit is

• A. \(30 \text{ V}\)
• B. \(60 \text{ V}\)
• C. \(50 \text{ V}\)
• D. \(110 \text{ V}\)

Hint:

Phasor addition must be used for AC voltages, not simple algebraic addition.

Answer 1

The Correct Option is C

Step 1: Formula
In an LCR series circuit, $E = \sqrt{V_R^2 + (V_L - V_C)^2}$.

Step 2: Identification
From the image (4P), let $V_R = 40 \text{ V}$, $V_L = 40 \text{ V}$, and $V_C = 10 \text{ V}$.

Step 3: Calculation
$E = \sqrt{40^2 + (40 - 10)^2} = \sqrt{40^2 + 30^2}$.
$E = \sqrt{1600 + 900} = \sqrt{2500} = 50 \text{ V}$.
Final Answer: (C)