Lesson 1 of 10 · 5 min

Alternating voltage and a resistor

NCERT §7.1, §7.2

Riya plugs her bench's 100 W, 220 V lamp into the mains. The voltage across it reverses a hundred times every second, yet the lamp glows steadily. What is the current doing?

The story this chapter follows: Riya's ac bench

Riya's bench runs off the 220 V, 50 Hz mains and a supply whose frequency she can turn. On it are a 100 W, 220 V lamp, a pure 25.0 mH coil, a 15.0 μF capacitor, a 200 Ω resistor, an LCR kit of 3 Ω, 25.48 mH and 796 μF, and a transformer with 100 and 200 turns. They are the parts from NCERT's worked examples, and every idea in this chapter is tried out on them.

The lesson in notes

In short

The mains supply is not steady: its voltage swings like a sine function of time. Such a voltage is an alternating (ac) voltage, and the current it drives is an alternating current.

AC is preferred for supply mainly because transformers can raise or lower ac voltages easily and efficiently, which also makes sending energy over long distances economical.

Take the source voltage as v = vm sin ωt, with amplitude vm and angular frequency ω.

Across a resistor R, Kirchhoff's loop rule gives vm sin ωt = iR, so i = im sin ωt with im = vm/R. Ohm's law holds for ac just as for dc.

Voltage and current in a resistor are in phase: they pass through zero, their maxima and their minima at the same moments.

Over a full cycle the current is positive for half the time and negative for the other half, so its average is zero. That does not make the heating zero, because the heating depends on i², which is never negative.