## Alternating Current (AC)

Alternating current is a type of electrical current where the flow of electric charge periodically reverses direction. In simple terms, the flow of electrons changes direction in a cyclical manner. This is different from direct current (DC), where the flow of electric charge remains constant in one direction. AC is the most common form of electricity used in homes and businesses worldwide.

## Voltage

Voltage, also known as electric potential difference, is the measure of potential energy per unit charge between two points in an electrical circuit. It represents the force or pressure that pushes electric charges through a conductor. Voltage is what causes electric charges to flow in a circuit. It’s typically measured in volts (V) and can be either positive or negative, depending on the direction of current flow.

In an AC circuit, the voltage alternates in polarity, meaning it changes direction over time. This periodic change in voltage creates the alternating current. The rate at which the voltage changes direction is called the frequency and is measured in Hertz (Hz). In most power systems, the frequency is typically 50 or 60 Hz, meaning the direction of the current changes 50 or 60 times per second, respectively.

AC power is advantageous for long-distance transmission because it can be easily stepped up or down using transformers, allowing for efficient transmission and distribution of electricity across power grids. Additionally, many electrical devices, such as motors and appliances, are designed to operate on AC power.

alternating current (AC) is a type of electrical current where the flow of charge periodically changes direction, while voltage represents the electric potential difference between two points in an electrical circuit, causing electric charges to flow. Together, AC voltage and current power much of our modern electrical systems.

## When an alternating current (AC) voltage is applied to a resistor

RMS Voltage (Vrms ): This is the effective voltage that produces the same heating effect in a resistor as an equivalent DC (Direct Current) voltage. Mathematically, for an AC voltage ( V(t) ), the RMS voltage is calculated as:

Where T is the period of the AC waveform.

Mean Value (Vmean): This is the average value of the voltage over one complete cycle. For a sinusoidal waveform, the mean value is zero because the positive and negative values cancel each other out over time. However, for a non-sinusoidal waveform, the mean value may not be zero.

Amplitude of Voltage (Vo): This is the maximum value of the voltage in the waveform. For a sinusoidal waveform, the amplitude is the peak value, which is equal to the RMS value multiplied by the square root of 2 .

Amplitude of Current (Io): When a resistor is connected to an AC voltage source, the current flowing through it will also be alternating. The amplitude of the current depends on the resistance of the resistor according to Ohm’s law ( Io = Vo/R).

For a sinusoidal AC voltage applied to a resistor, the voltage and current waveforms will be in phase, meaning they reach their maximum and minimum values at the same time. The relationship between voltage, current, and resistance is given by Ohm’s law (V = IR ), where V is voltage, I is current, and R is resistance

## Phasor

Phasors are rotating vectors used to represent the amplitude and phase of alternating current or voltage in an AC circuit.

– A phasor is a vector that rotates in a circular motion at a constant angular velocity.

– The length of the phasor represents the amplitude or magnitude of the alternating quantity (current or voltage), and the angle it makes with a reference axis represents the phase difference with respect to a reference point in time.

Representation

– AC currents and voltages can be represented as phasors, simplifying the analysis of AC circuits.

– Suppose we have an AC voltage source. We can represent its voltage as a phasor where the length of the phasor represents the maximum voltage (amplitude) and its angle represents the phase difference with respect to a reference.

– Similarly, AC currents in a circuit can be represented as phasors where the length represents the maximum current and the angle represents the phase difference between current and voltage.

Advantages

– Phasor representation simplifies the analysis of AC circuits, especially when dealing with complex circuits containing multiple AC sources and components like resistors, capacitors, and inductors.

– Using phasors, calculations involving AC quantities can be treated similarly to DC circuits, making analysis more intuitive and straightforward.

Mathematical Representation

– Mathematically, phasors are represented using complex numbers, where the real part represents the magnitude (amplitude) and the imaginary part represents the phase.

Phasors can be manipulated using phasor algebra, which involves addition, subtraction, multiplication, and division of phasors to solve AC circuit problems.

Overall, phasors provide a convenient and powerful tool for analyzing alternating current circuits, enabling engineers and physicists to understand and design complex electrical systems more effectively.