Alternating Current

Direct current flows one way and keeps its value. Alternating current reverses direction periodically, and in the mains supply it does so smoothly, following a sine wave.

Two numbers describe it. The frequency is how many complete cycles pass each second — 50 Hz in Pakistan, so the current reverses a hundred times a second and completes fifty full cycles. The peak value is the maximum it reaches in either direction.

The average value over a whole cycle is zero, because the negative half exactly cancels the positive. That makes the ordinary average useless for describing a.c., and it is why a different kind of average is needed.

Power does not care which way the current flows. Heating goes as I²R, and squaring makes the negative half positive — so an alternating current heats a resistor perfectly well even though its average is zero.

The useful measure is therefore the root mean square: square the values, take the mean of those squares, then take the square root. That undoes the cancellation and leaves a number that predicts power correctly.

For a sine wave the arithmetic works out to peak divided by √2, about 0.707 of the peak. Every a.c. value you meet in ordinary life is an RMS value unless it says otherwise.

So Pakistan's 230 V mains actually peaks at about 325 V, and swings between +325 V and −325 V. Insulation has to withstand the peak; the heating is set by the RMS. That is the practical reason the distinction matters.

V_rms

root mean square voltageV

V_peak

peak voltageV

P

average powerW

The dashed lines mark either the RMS or the peak. Notice the RMS line sits well inside the peak — at about 0.707 of it. It is not an average of the wave; it is the steady value that would heat a resistor at the same rate.

A resistor behaves the same whether the current is steady or alternating. Two other components do not, and both oppose alternating current in a way that depends on frequency.

A capacitor blocks direct current completely — no charge crosses the gap between its plates. But with alternating current the plates charge and discharge repeatedly, so current flows in the circuit continuously. The opposition, called capacitive reactance, falls as frequency rises: the faster the reversals, the less time there is for charge to build up and oppose the flow.

An inductor is a coil, and it opposes any change in current by inducing a back e.m.f. — Lenz's law again. Its opposition, inductive reactance, rises with frequency, because faster changes induce a larger opposing e.m.f.

The two behave in exactly opposite ways, which is what makes the next section possible. It is also why a capacitor passes a treble signal while an inductor passes bass — the basis of the crossover in a loudspeaker.

X_C

capacitive reactanceΩ

X_L

inductive reactanceΩ

C

capacitanceF

L

inductanceH

Z

impedanceΩ

Put a resistor, a capacitor and an inductor in series and sweep the frequency. At one particular frequency the two reactances become equal and cancel, leaving only the resistance. The current then reaches its maximum, and the circuit is at resonance.

A resonant circuit responds strongly to one frequency and weakly to all others, which is exactly what tuning means. Turning the dial on a radio changes a capacitance, moving the resonant frequency until it matches the station you want; every other station is still arriving at the aerial but produces almost no current.

Finally, the reason the grid runs on alternating current at all. Transformers only work on a.c., because they depend on a changing magnetic field. Transformers allow the voltage to be stepped up for transmission, and since P = VI, a high voltage means a small current for the same power delivered.

That matters because the heat lost in the cables is I²R. Cutting the current by a factor of ten cuts the loss by a factor of a hundred. Transmitting at 500 kV instead of 230 V is the difference between losing a few per cent of the power and losing nearly all of it — and none of that is possible with d.c. and no transformers.

f₀

resonant frequencyHz

L

inductanceH

C

capacitanceF