AIIMS2019Physics-Electromagnetism

AIIMS 2019 Physics AC Circuits MCQ Question

Type: MCQ-conceptual-Medium-Class 12

In an LCR series circuit, the source voltage is 120 volt120\text{ volt}, the voltage across the inductor is 50 volt50\text{ volt}, and across the resistor is 40 volt40\text{ volt}. Determine the voltage across the capacitor.

A

Vc=10(582)\text{V}_\text{c} = 10\left(5 - 8\sqrt{2}\right)

B

Vc=10(5+82)\text{V}_\text{c} = 10\left(5 + 8\sqrt{2}\right)

C

Vc=20(5+82)\text{V}_\text{c} = 20\left(5 + 8\sqrt{2}\right)

D

Vc=10(5+72)\text{V}_\text{c} = 10\left(5 + 7\sqrt{2}\right)

Correct Answer

Option B

Detailed Explanation

In an LCR circuit, the phasor diagram illustrates the relationship between the voltage and current across the inductor (L), capacitor (C), and resistor (R). Option B is correct because it accurately represents the phase differences, showing that the total voltage phasor is the vector sum of the individual voltage phasors across each component, which is essential for understanding impedance and resonance in AC circuits. The other options are incorrect as they may misrepresent the phase relationships or fail to include critical components of the circuit, leading to an incomplete understanding of the circuit's behavior. Understanding these phase relationships is crucial for analyzing how reactive components affect overall circuit performance.

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