Alternating Current — Part 2: LCR circuits, power, generators and transformers: visual lesson, CBSE Class 12 Physics

Lesson

LCR circuits, power and transformers

Part 2 — combining R, L and C in series, resonance, the power actually used in AC circuits, and the machines that make and transform AC.

In this lesson you will

Find the impedance and phase angle of a series LCR circuit using phasors
Explain resonance and calculate the resonant frequency
Calculate average power, explain power factor and wattless current
Explain the working of an AC generator and a transformer

Diagram

Series LCR circuit: phasor diagram

Drawn to scale from the worked example; angle checked against atan((XL − XC)/R).

The same current $I$ flows through all three. Take $I$ as reference: $V_R = IR$ in phase, $V_L = IX_L$ ahead by 90°, $V_C = IX_C$ behind by 90°. Adding the phasors: $V = \sqrt{V_R^2 + (V_L - V_C)^2} = I\sqrt{R^2 + (X_L - X_C)^2}$

Concept

Impedance and phase angle

$Z = \sqrt{R^2 + (X_L - X_C)^2},\qquad I = \dfrac{V}{Z},\qquad \tan\phi = \dfrac{X_L - X_C}{R}$ $\phi$ is the angle by which the voltage leads the current.

$X_L > X_C$ : inductive circuit, V leads I.
$X_C > X_L$ : capacitive circuit, I leads V.
$X_L = X_C$ : resistive, in phase (resonance).

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