Question

If \( V_L, V_R, V_C \), and \( V_O \) are readings of AC voltmeter across the inductor, resistor, capacitor, and source respectively in a certain L-C-R circuit, then: 
 

• A. \( V_O = V_L + V_R + V_C \)
• B. \( V_O = (V_L - V_C) + V_R \)
• C. ( \( V_O^2 = V_L^2 + V_R^2 + V_C^2 \)
• D. \( V_O^2 = (V_L - V_C)^2 + V_R^2 \)

Hint:

Use the phasor addition technique to derive voltage relationships in L-C-R circuits.

Answer 1

The Correct Option is D

In an L-C-R circuit, the voltage \(V_O\) of the source is the vector sum of voltages across the resistor (\(V_R\)), inductor (\(V_L\)), and capacitor (\(V_C\)). Due to phase differences, the net voltage satisfies: \[ V_O^2 = (V_L - V_C)^2 + V_R^2. \]