Ch 7Alternating Current — concept-first.

So far, you have studied direct current (dc) — where charges flow steadily in one direction. In dc circuits, the voltage and current are constant in time.

When an alternating voltage is applied across a pure resistor, the current that flows is also alternating.

For a resistor, current and voltage rise and fall together — they are in phase. But for inductors, capacitors, or combinations, the current and voltage reach their peaks at different times.

When an AC voltage is applied to a pure inductor (one with negligible resistance), the inductor does not oppose current in the same way a resistor does.

In a DC circuit, a capacitor charges quickly and then blocks current completely — the current stops once the capacitor is fully charged.

Consider a series circuit with an inductor (), a capacitor (), and a resistor () connected to an AC source. The source voltage varies sinusoidally with time:

In a series LCR circuit, the current through the resistor, inductor, and capacitor is the same at every instant.

Resonance is a phenomenon that occurs in any system that has a natural frequency — the frequency at which it prefers to oscillate.

For a series RLC circuit driven by a sinusoidal voltage , the resulting current is , where is the phase angle between voltage and current.

In the transmission and use of electrical power, we often need to change an alternating voltage to a higher or lower value.

- Root Mean Square (RMS) Values: For a sinusoidal AC, and , where and are peak values. RMS value gives the equivalent DC heating effect.

1. When an AC voltage or current value is given without qualification, it is always the rms value. For example, the 240 V from a household outlet is the rms voltage. The peak amplitude is .

The end-of-chapter exercises from the NCERT textbook.

Higher-order thinking problems from the NCERT Exemplar.