In an L C R series circuit, the voltage across each of the...

In an $L C R$ series circuit, the voltage across each of the components $L, C$ and $R$ is $50 \mathrm{~V}$. The voltage across the $L C R$ combination will be
(a) $0 \mathrm{~V}$
(b) $50 \mathrm{~V}$
(c) $50 \sqrt{2} \mathrm{~V}$
(d) $100 \mathrm{~V}$

Key Concepts

Phasor Addition

In AC circuits, the voltages across different components are represented as phasors—vectors that have magnitude and phase angle. This representation is essential because the individual voltages may not be oriented in the same direction in the complex plane. When analyzing a series circuit, the overall voltage is determined by the vector (phasor) sum of the individual voltages rather than a simple algebraic sum.

Voltage Cancellation in Reactive Components

Inductive and capacitive elements in AC circuits produce voltages that are phase shifted by ±90° relative to the current. When an inductor and a capacitor in series have equal voltage magnitudes, their phasors are oppositely directed, leading to cancellation. This phenomenon is particularly important in resonance conditions and ensures that the net reactive voltage can be minimized or even reduced to zero, leaving only the resistive voltage to be considered.

RMS Voltage and AC Circuit Analysis

Root Mean Square (RMS) voltage is the effective value of a varying AC voltage. In AC circuit analysis, the RMS values are used for power calculations and for comparing circuit quantities. When combining RMS voltages from different components in a circuit, it is crucial to consider their phase relationships, leading to the necessity of phasor addition rather than simple arithmetic addition.

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