Alternating Current | Class 12 Physics Notes
By ConceptScroll Team · Published on 17 July 2026 · 2 min read
Alternating Current – this guide gives you a concise, exam-ready overview of Alternating Current from Class 12 Physics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.
7.6 AC VOLTAGE APPLIED TO A SERIES LCR CIRCUIT
This section studies the behavior of a series circuit containing a resistor (R), inductor (L), and capacitor (C) connected to an AC voltage source v = v_m sin ωt. Using Kirchhoff's loop rule, the voltage equation is L (di/dt) + i R + q / C = v. The current i has the same amplitude and phase throughout the series circuit and is expressed as i = i_m sin (ωt + φ), where φ is the phase difference between source voltage and current. Using phasor analysis, voltage phasors across R, L, and C are represented: V_R is in phase with current I, V_L leads I by π/2, and V_C lags I by π/2. The net voltage V is the phasor sum of these voltages. Applying Pythagoras theorem, the impedance Z is defined as Z = sqrt(R² + (X_C - X_L)²), where X_L = ωL and X_C = 1/(ωC). The current amplitude is i_m = v_m / Z. The phase angle φ = tan⁻¹((X_C - X_L)/R) determines whether the circuit is inductive (current lags voltage) or capacitive (current leads voltage). The section discusses resonance occurring when X_L = X_C, resulting in minimum impedance Z = R and maximum current i_m = v_m / R. The resonant frequency is ω_0 = 1 / sqrt(LC). Examples illustrate calculations of current, voltages, and resonance in series LCR circuits. The section also explains the practical importance of resonance in tuning circuits like radios.
📊 Diagram: See figure_12: Series LCR circuit connected to AC source; figure_13(a) and (b): Phasor relations of voltages and current; figure_14: Impedance diagram; figure_15: Phasor diagram and voltage-current graphs for X_C > X_L; figure_16: Variation of current amplitude with frequency for different resistances.
🔗 Connection: Leads to the study of power in AC circuits and the concept of power factor.
Frequently asked questions
What is the resistance offered by a pure inductor for DC?
zero
If the power factor of LCR circuit is one then the circuit is purely
resistive
A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of smaller radius, having ‘n’ turns. The magnetic field at the centre of the coil will be
n 2 B
When an AC is connected to a resistor what is the phase difference between the current and voltage?
0 0
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