In an LCR series ac circuit the voltage across each of the...

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

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Key Concepts

LCR Series Circuit

An LCR series circuit is an alternating current (AC) circuit that contains an inductor (L), a capacitor (C), and a resistor (R) connected in series. Its analysis involves understanding how each component contributes to the total voltage and current in the circuit, with the resistor dissipating energy, the inductor storing energy in a magnetic field, and the capacitor storing energy in an electric field.

Phasor Representation in AC Analysis

Phasor diagrams are used in AC circuit analysis to represent the magnitude and phase angles of sinusoidal signals. They allow for a visual understanding of how voltages and currents in different components, which may be out of phase, combine through vector addition, providing insight into the overall circuit behavior.

Reactance Cancellation

In AC circuits, the inductive reactance (due to the inductor) and the capacitive reactance (due to the capacitor) are equal in magnitude but opposite in phase. When these two are in series, their effects can cancel each other out, a phenomenon that is pivotal in analyzing circuits where the net reactive voltage or impedance is reduced or nullified.

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