What traumatic event does Zitkala-Sa describe at the school?

The forcible cutting of her long hair

Why was the cutting of her hair so humiliating to Zitkala-Sa?

Among her people, shingled hair was worn by cowards and mourners

Why is rms value used for alternating current?

Because the average of AC over a cycle is zero; rms gives the equivalent steady heating value.

Relate peak and rms values.

\(i_{rms}=i_0/\sqrt{2}\) and \(V_{rms}=V_0/\sqrt{2}\) for sinusoidal AC.

What is the phase relation in a purely inductive circuit?

Current lags the voltage by \(90^\circ\); reactance is \(X_L=\omega L\).

What is the phase relation in a purely capacitive circuit?

Current leads the voltage by \(90^\circ\); reactance is \(X_C=1/\omega C\).

Write the impedance of a series LCR circuit.

\(Z=\sqrt{R^2+(X_L-X_C)^2}\), and \(\tan\phi=(X_L-X_C)/R\).

What is the resonant frequency of an LCR circuit?

\(\omega_0=\dfrac{1}{\sqrt{LC}}\), where \(X_L=X_C\) and current is maximum.

What is average power in an AC circuit?

\(P=V_{rms}I_{rms}\cos\phi\); the factor \(\cos\phi\) is the power factor.

What is a wattless current?

A current \(90^\circ\) out of phase with voltage, delivering zero average power.

How does a transformer change voltage?

By the turns ratio: \(\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}\) in an ideal transformer.

Why is AC preferred for power transmission?

It is easily stepped up to high voltage by transformers, reducing \(I^2R\) losses over long lines.

Alternating Current

Class 12 Physics · Physics Part I · Chapter 7

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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:

Flashcards & interactive practice