20.5 Alternating Current versus Direct Current

Alternating Current versus Direct Current

Alternating Current (AC) and Direct Current (DC) are the two fundamental types of electrical flow. AC periodically reverses direction, while DC maintains a constant flow in one direction. Understanding their differences matters because it explains why your wall outlet delivers AC, why your phone battery uses DC, and why the power grid is designed the way it is.

Alternating Current (AC) and Direct Current (DC)

AC vs DC Characteristics

Alternating Current (AC) reverses direction periodically, flowing back and forth in a sinusoidal (wave-like) pattern. The voltage swings between positive and negative values over time, completing full cycles at a steady rate.

• Typically generated by rotating generators or alternators that convert mechanical energy into electrical energy
• Can be stepped up or down to different voltage levels using transformers, which makes long-distance transmission practical
• Characterized by its frequency, measured in Hertz (Hz). In the U.S., AC runs at 60 Hz (60 complete cycles per second); in most of Europe, it's 50 Hz.
• Powers household electrical systems (outlets, appliances) and the entire electrical grid

Direct Current (DC) flows in a single, constant direction from the negative terminal to the positive terminal (by convention, we often describe conventional current as flowing from positive to negative, but the electrons physically move the other way).

• Voltage polarity stays fixed, with a constant positive and negative terminal
• Produced by batteries (AA, lithium-ion), solar cells (photovoltaic panels), and rectifiers (devices that convert AC to DC)
• Cannot be easily transformed to different voltage levels without specialized electronic circuits (DC-DC converters)
• Powers electronic devices (smartphones, laptops), battery-operated systems (flashlights, remote controls), and certain industrial processes (electroplating, welding)

RMS Values in AC Circuits

Because AC voltage constantly changes, you need a way to describe its "effective" value. That's where Root Mean Square (RMS) comes in. The RMS value of an AC waveform is the equivalent DC voltage (or current) that would deliver the same power (the same heating effect) to a resistor.

For a sinusoidal waveform, the RMS formulas are:

$V_{rms} = \frac{V_0}{\sqrt{2}}$

$I_{rms} = \frac{I_0}{\sqrt{2}}$

where $V_0$ and $I_0$ are the peak (maximum) values, and $\sqrt{2} \approx 1.414$.

When someone says a U.S. household outlet is "120 V," that's the RMS voltage. The peak voltage is actually higher:

$V_0 = V_{rms} \times \sqrt{2} = 120\text{ V} \times 1.414 \approx 170\text{ V}$

So the voltage at your outlet swings between about +170 V and −170 V, but its effective (RMS) value is 120 V.

Calculating RMS step by step:

1. Identify the peak value of the voltage or current (from a graph, a problem statement, or a known source).
2. Divide the peak value by $\sqrt{2}$ to get the RMS value.
3. Use the RMS value in power calculations, since $P = I_{rms} \times V_{rms}$ for a purely resistive load.

Advantages of AC Power Transmission

AC dominates long-distance power transmission for a few key reasons, all connected to each other.

Voltage transformation is simple. Transformers can step AC voltage up or down with no moving parts, just coils of wire wrapped around an iron core. This means power plants can step voltage up to very high levels (100 kV or more) for transmission, then step it back down to 120 V or 240 V for safe use in homes and businesses.

High voltage means lower current, which means less energy wasted. For a given amount of power, raising the voltage reduces the current, since $P = VI$. This matters because power lost as heat in the transmission wires depends on the square of the current:

$P_{loss} = I^2 R$

Cutting the current in half reduces transmission losses by a factor of four. That's why power companies transmit at hundreds of thousands of volts over long distances.

Generation and distribution are more practical. AC generators (alternators) are mechanically simpler and more robust than DC generators. The grid also uses three-phase AC, where three AC waveforms are offset by 120° from each other. Three-phase systems deliver power more smoothly and efficiently, which is especially useful for running large industrial motors.

All of this rests on electromagnetic induction, the principle that a changing magnetic field induces a voltage in a conductor. Induction is what makes both generators and transformers work.

AC Circuit Analysis

At the introductory level, you should be aware of a few terms that come up when analyzing AC circuits beyond simple resistors:

• Impedance ($Z$): The total opposition to current flow in an AC circuit. It combines regular resistance ($R$) with reactance, which is the opposition caused by capacitors and inductors. Impedance is measured in ohms.
• Power factor: The ratio of real power (the power actually consumed) to apparent power (the product of RMS voltage and RMS current). A power factor of 1 means all the power is being used productively; a lower value means some power is "wasted" cycling back and forth in the circuit.
• Phase angle: The time offset between the voltage and current waveforms. In a purely resistive circuit, voltage and current are in phase (phase angle = 0°). Capacitors and inductors cause the current to lead or lag the voltage, which affects the power factor.

These concepts become central in more advanced circuits courses, but for now, the main takeaway is that AC circuits with capacitors or inductors behave differently from simple DC resistor circuits.