CBSE Class 12 — Notes, Chapters & Practice Quizzes

Chapter 7: Alternating Current

Summary

Alternating current reverses direction periodically, varying as \(i=i_0\sin\omega t\). Because its average over a cycle is zero, we use the root-mean-square value \(i_{rms}=i_0/\sqrt{2}\), which gives the same heating as a steady current. In an AC circuit a resistor keeps current in phase with voltage, an inductor makes current lag by \(90^\circ\) with reactance \(X_L=\omega L\), and a capacitor makes current lead by \(90^\circ\) with reactance \(X_C=1/\omega C\). In a series LCR circuit the impedance is \(Z=\sqrt{R^2+(X_L-X_C)^2}\) and the current lags or leads the voltage by a phase angle \(\tan\phi=(X_L-X_C)/R\). Resonance occurs when \(X_L=X_C\), at \(\omega_0=1/\sqrt{LC}\), where impedance is minimum and current maximum—vital for tuning circuits. Average power is \(P=V_{rms}I_{rms}\cos\phi\), the power factor \(\cos\phi\) determining useful power; a purely reactive (wattless) current delivers no average power. Transformers, working by mutual induction, step voltage up or down by the turns ratio, enabling efficient long-distance power transmission.

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