Alternating Current
Class 12 Physics · Physics Part I · Chapter 7
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Accountancy
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اردو (اختیاری)
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Mathematics
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हिंदी (आधार)
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संस्कृतम् (केन्द्रिकम्)
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हिंदी (ऐच्छिक)
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संस्कृत (ऐच्छिक)
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हिंदी (ऐच्छिक)
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اردو (کور)
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Chemistry
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Urdu Elective
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Computer Science
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Chemistry
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Fine Art · Painting
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हिंदुस्तानी संगीत (गायन / वादन)
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Biology
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Informatics Practices
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Accountancy
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Biotechnology
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सृजनात्मक लेखन और अनुवाद
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हिंदुस्तानी संगीत (तबला / पखावज)
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Economics
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History
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History
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History
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Geography
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English Core · Flamingo
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Home Science
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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.
AC and rms valuesAC through R, L and CSeries LCR circuit and impedanceResonancePower and power factorTransformers and transmission
Key terms
RMS value
Effective value of AC, \(i_{rms}=i_0/\sqrt{2}\), giving equal heating to DC.
Reactance
Opposition of inductor (\(X_L=\omega L\)) or capacitor (\(X_C=1/\omega C\)) to AC.
Impedance
Total opposition in an AC circuit, \(Z=\sqrt{R^2+(X_L-X_C)^2}\).
Resonance
Condition \(X_L=X_C\) at \(\omega_0=1/\sqrt{LC}\) giving maximum current.
Power factor
Cosine of the phase angle, \(\cos\phi\), fixing useful average power.
Transformer
Device using mutual induction to change AC voltage by the turns ratio.
Extra questions & answers
Try one from this chapter
The rms value of a sinusoidal current of peak value \(i_0\) is: