AC Electricity: Fundamentals and Applications

Introduction to Alternating Current (AC) and Direct Current (DC)

Electricity can be supplied as either direct current (DC) or alternating current (AC). DC maintains a constant direction and magnitude, while AC periodically reverses direction and varies in magnitude, typically in a sinusoidal pattern.

• Direct Current (DC): Current flows in one direction only; voltage is constant.

• Alternating Current (AC): Current reverses direction periodically; voltage oscillates sinusoidally.

• Source of AC: Generated by rotating a coil in a magnetic field (e.g., electric generators).

Example: Household electricity is supplied as AC, typically at 60 Hz in the United States.

Mathematical Description of AC Voltage and Current

The instantaneous emf (voltage) of an AC source is given by:

• = peak emf (volts)

• = period (seconds)

• = frequency (Hz)

Example: In the US, wall outlets provide AC with a peak voltage of about 170 V and a frequency of 60 Hz.

Notation in AC Circuits

Capital letters denote constant quantities; lowercase letters denote time-varying quantities.

• DC Ohm's Law:

• AC Ohm's Law:

AC Circuits with Resistors

Resistor in an AC Circuit

When a resistor is connected to an AC source, the voltage and current both oscillate sinusoidally and remain in phase.

• Kirchhoff's loop rule applies:

• Ohm's Law for AC:

• Current and voltage reach their maxima and minima simultaneously (in phase).

Power in AC Resistor Circuits

The instantaneous power dissipated in a resistor is:

• Power oscillates at twice the frequency of the voltage/current.

• Average power:

Root-Mean-Square (RMS) Values

To compare AC and DC values, we use the root-mean-square (rms) value, which represents the equivalent DC value that would produce the same power dissipation.

• Average power:

Example: For a US wall outlet, V, so V.

Transformers and Power Transmission

Principle and Construction of Transformers

A transformer is a device that changes the voltage of AC electricity using electromagnetic induction. It consists of two coils (primary and secondary) wound on an iron core.

• Primary coil: turns, connected to input voltage

• Secondary coil: turns, output voltage

• Operation requires AC (changing magnetic flux)

Transformer Equations

• Voltage ratio:

• Current ratio:

• Power conservation (ideal transformer):

• Step-up transformer: (increases voltage, decreases current)

• Step-down transformer: (decreases voltage, increases current)

Power Transmission and Efficiency

Electricity is transmitted at high voltages to minimize power loss in transmission lines, which is proportional to the square of the current (). Transformers are essential for stepping up and down voltages for efficient transmission and safe usage.

Household Electricity and Safety

Grounding and Electrical Outlets

Grounding provides a reference potential (0 V) and a safe path for current in case of faults. Household outlets have a hot side (120 V AC) and a neutral side (grounded).

Circuit Protection: Fuses and Circuit Breakers

To prevent overheating and fire, circuits are protected by fuses or circuit breakers, which disconnect the circuit if the current exceeds a safe value.

• Fuse: Melts and breaks the circuit when current is too high (must be replaced).

• Circuit breaker: Electromechanical device that can be reset after tripping.

Parallel Wiring and Circuit Overload

Household outlets are wired in parallel, so each device receives the full voltage. Overloading occurs when too many devices draw excessive current, risking tripping the breaker or causing fire.

Energy Consumption: Kilowatt-Hours

Electric energy usage is measured in kilowatt-hours (kWh):

• 1 kWh = J

• Energy (kWh) = Power (kW) × Time (h)

Electrical Safety and Biological Effects

Physiological Effects of Electric Current

The danger of electric shock depends on the current passing through the body, not just the voltage. AC is generally more dangerous than DC for the same current.

Body Resistance and Protective Measures

The human body can be modeled as a network of resistors. Skin resistance is much higher than internal body resistance, and protective equipment (e.g., rubber boots) greatly increases total resistance, reducing dangerous current flow.

Special Cases: Birds on Power Lines

Birds can safely perch on high-voltage lines because the potential difference between their feet is negligible, so little or no current flows through their bodies.

Ground Fault Interrupters (GFI)

GFI outlets detect differences between hot and neutral currents and disconnect the circuit if a ground fault is detected, providing enhanced safety in wet environments.

Summary Table: Key AC Circuit Quantities

Additional info:

• Inductors and capacitors introduce reactance in AC circuits, causing phase differences between voltage and current (not covered in detail here).

• Transformers only work with AC due to the need for changing magnetic flux.