Alternating Current

Alternating Current and Direct Current are the two types of electricity based on the direction of the voltage and current. In households, we use mostly Alternating Current as the grids are designed to provide alternating current only. But in the case of power storage, DC is used. Alternating currents vary with time so does their voltage.

All the appliances in a common household are wired to work with these types of currents and voltage sources. To understand the workings of these devices in real life, it becomes essential to understand the concepts behind alternating current (AC). Let’s look at these concepts in detail.

What is Alternating Current (AC)?

Alternating current (AC) is a type of electric current that periodically changes direction i.e., flowing in one direction first and then changing its direction to opposite to the initial flow.

Unlike Direct current which flows in one specific direction, alternating current constantly oscillates back and forth at some fixed frequency. In most countries, this frequency is either 50 Hz or 60 Hz.

Alternating Current Definition

Alternating Current is defined as the flow of electric charge that changes direction periodically. 

Alternating current (AC) is characterized by the voltage that is also varying and current waveforms that oscillate between positive and negative values.  AC is commonly used for large-scale electrical power generation, transmission, and distribution that powers a wide range of devices in a common household. 

Alternating Current Voltage Symbol

The alternating current voltage symbol or alternating current symbol consists of a circle with a sine wave inside it where the sine wave within the circle represents the waveform of the alternating current (AC) being generated by the source.

AC Generators

Alternating currents can be generated using devices which are known as alternators. Apart from these, there are many circuits that are able to produce alternating voltages and currents.

One of the most basic ways to produce an AC voltage or current is by using a single-coil AC generator. The generator consists of two-pole magnets and a single loop of wire which has a rectangular shape. For supplying AC, the following three wires are used:

• Hotwire for power transmission.
• The neutral wire is connected to the earth, this wire provides a return path for the current in the hot wire.
• The third wire is connected to the earth and is linked to the metallic parts to avoid electric shock hazards.

Learn more about AC Generators

Alternating Current Waveform

The AC current forms a wave similar to the sinusoidal wave, the wave starts from zero and reaches its maximum value then started decreasing to reach the zero value it continues to decrease till it reaches its minimum value(negative maximum value) and then it increases again to reach the zero value. The AC waveform is positive in the first half and negative in the second half.

Characteristics of Alternating Current (AC)

There are various characteristics of alternating current, some of these are listed as follows:

• Sinusoidal Waveform
• Frequency and Amplitude
• Alternating Current Average Value
• Alternating Current Peak Value
• Alternating Current RMS Value
• Phase and Phase Difference

Let’s discuss these characteristics in detail.

Sinusoidal Waveform

Alternating current has a waveform that varies smoothly and is periodic with time and also looks like a sine wave.

Due to these all features of the waveform, it resembles a sine wave and represents the instantaneous value of the current or voltage over time. The alternating current waveform is called sinusoidal waveform due to its similarity with the sine wave.

Frequency and Amplitude

Frequency of an AC sinusoidal waveform refers to the number of complete cycles it completes per second and is measured in Hertz (Hz). In many power systems, the standard frequency is 50 or 60 Hz. The amplitude of an AC waveform represents the maximum value of the current or voltage reached during each cycle.

Alternating Current Peak Value

The peak value of an AC waveform refers to the maximum positive or negative value reached during each cycle. It represents the highest magnitude of the waveform. Generally, this is represented as I_m or I₀.

Alternating Current Average Value

Compared to DC, AC doesn’t have a constant value, as it oscillates. Thus, we use the average value of AC over a half cycle, as for the complete cycle average value is 0 because positive and negative halves cancel each other out. The mathematical Formula for the average value of AC for a positive half cycle is:

I_av = 2I_m/π

Where,

• I_av is the average value of AC, and
• I_m is the peak value of AC.

Alternating Current Root Mean Square (RMS) Value

RMS value is the value of DC which is flowing through the conductor to produce the same amount of heat as AC is flowing through the same conductor, due to this RMS value is also called the Effective Value of a sinusoidal AC. Mathematically RMS Value of AC is given as

I_rms = I_m/√2

Where,

• I_rms is the RMS value of AC, and
  • I_m is the peak value of AC.

Learn more about Root Mean Square

Phase and Phase Difference

In AC systems, multiple waveforms may be present, and they can have a phase difference with respect to each other. The phase refers to the relative position of one waveform compared to another.

Phase difference is usually measured in degrees or radians. The phase difference between two AC waveforms indicates the angular displacement between them. It determines how the waveforms align with each other in time.

Alternating Current Vs Direct Current

Alternating current and DC current have major differences between them. Some key  differences between direct current and alternating current are as follows:

Parameter	Alternating Current (AC)	Direct Current (DC)
Direction of flow	Reverses direction periodically	Flows in one direction only
Voltage	Voltage magnitude varies with time	Voltage remains constant
Power Transmission	Efficient over long distances	Requires conversion for long-distance transmission
Generation	Easily generated through AC generators	Requires conversion from AC or battery
Transmission Lines	AC lines use transformers for voltage control	DC lines require less infrastructure
Energy storage	Challenging due to continuous voltage changes	Easily stored in batteries or capacitors
Appliances	Suitable for most household and industrial uses	Used in electronic devices and certain industries
Electrical Safety	Higher risk of electric shock due to voltage changes	Lower risk of electric shock due to constant voltage
Conversion	Can be converted to DC using rectifiers	Can be converted to AC using inverters
Historical usage	Predominant in power grids and homes	Used in early electrical systems and batteries

AC Circuit Analysis

There are some key concepts we need to know before the analysis of AC circuits, such as reactance, impedance, phasor diagram, etc. Let’s learn about these concepts in detail as follows:

Reactance and Impedance

Reactance is the resistance offered by various electronic components in an AC Circuit due to its stored energy or capacitance. Reactance is measured in Ohms similar to resistance and is denoted by “X”. Reactance is frequency-dependent and differs for capacitive and inductive components.

Impedance, on the other hand, is a more general term that is used to define the combined effect of both resistance and reactance in an AC circuit. It represents total opposition to the flow of alternating current. Impedance is also measured in ohms and is denoted by the symbol “Z.”

Ohm’s Law for AC Circuits

Ohm’s Law for AC circuits is an extension of Ohm’s Law, which applies to DC circuits. Ohm’s Law for AC circuits relates the current, voltage, and impedance in an AC circuit, and  Mathematically, Ohm’s Law for AC circuits is expressed as:

V = I × Z

Where,

• V is the RMS value of voltage across the circuit (in volts),
• I is the RMS value of current (in amperes), and
• Z is the impedance of the circuit (in ohms).

AC Circuit with only Resistance

The figure given below shows an alternating voltage source being applied to a resistor that is connected in series with the source. 

The source produces a sinusoidal varying potential difference across its terminals. Let us assume that this potential difference is called AC voltage. Then, this sinusoidally varying voltage can be expressed by the equation given below, 

v = v_msinωt 

Here, v_m is the amplitude of the oscillating voltage and ω denotes its angular frequency. 

The amplitude of the current in the given circuit is given by, 

i = 

The figure given below plots both of the values on the graph. Notice that both current and voltage go to maximum and become zero at the same time. This means that they have zero phase difference. 

It can be inferred from the figure that the average current is also zero in a single cycle is zero. 

AC Circuit with only Capacitor

Capacitive Reactance (X_c): Capacitors store electrical energy in an electric field. In an AC circuit, the capacitor charges and discharges, creating a reactance that opposes the current flow. The formula for capacitive reactance is,

X_c = 1 / (2πfC)

Where,

• “f” is the frequency of the AC signal in hertz
• “C” is the capacitance in farads

AC Circuit with only Inductor

Inductive Reactance (X_L): Inductors store energy in a magnetic field. In an AC circuit, the changing magnetic field induces a voltage that opposes the current flow. The formula for inductive reactance is,

X_L = 2πfL

Where,

• “f” is the frequency of the AC signal in hertz
• “L” is the inductance in Henries

Power Dissipation in AC Circuit

Even though the average current through the cycle is zero, that does not mean that the average power dissipation through the cycle is also zero. Dissipation of electrical energy is there. It’s known that Joule’s heating is given by I²R and depends on I². This term is always positive irrespective of the sign of “i”. Thus average dissipation cannot become zero. 

P = (I_m)²sin²ωtR

This is the instantaneous power in the circuit. Average power dissipation is given by, 

P_avg = 1/2(I_m)²R = (V_m)²/2R

Expressing this expression of power similar to the usual expression. 

P_avg = I²R = V²/R

Where,

• I is RMS value of Current i.e., , and 
• V is RMS value of Voltage i.e., .

Applications of Alternating Current

There are various use cases of Alternating Current, some of these use cases are as follows:

• In electrical networks, AC is utilized for power distribution.
• Due to their efficiency and ability to modulate speed, AC motors are frequently utilized in industrial applications.
• In today’s world, all the major electrical equipment is designed to work on AC, such as cooling systems, LED lights, Washing Machines, etc.
• In communication systems, like telephony and data transmission, AC signals are used.
• Medical equipment like X-ray machines and MRI scanners require AC electricity to operate.

Safety Considerations for Alternating Current

When working with alternating current (AC), there are several safety considerations to keep in mind. Some of these safety measures are:

• Ensure electrical isolation: Turn off the power supply and disconnect circuits before working on electrical equipment.
• Use lockout/tagout procedures: Prevent accidental energization while working on electrical equipment.
• Wear appropriate PPE: Insulated gloves, safety glasses, and protective clothing protect against electric shocks and arc flashes.
• Install GFCIs: In wet or damp areas like bathrooms and kitchens, use ground fault circuit interrupters to quickly interrupt the circuit in case of a ground fault.
• Implement overcurrent protection: Circuit breakers or fuses prevent excessive current flow during short circuits or overloads. Match the rating to the circuit requirements.
• Engage qualified personnel: For complex electrical work, involve electricians or individuals with appropriate training and knowledge to ensure compliance with electrical codes and safety standards.

Read More,

• Power in AC Circuit
• AC Generator
• How to Convert AC to DC?

Sample Problems on Alternating Current

Problem 1: A light bulb is rated at 100W for a 200V supply. Find the resistance of the bulb. 

Solution: 

Average power is given by, 

P = V²/R

Given,

• V = 200 
• R =? 
• P = 100 

Plugging these values into the equation, 

P = V²/R

⇒ 100 = (200)² /R 

⇒ R = 400 Ohms

Problem 2: Find the expression for the current flowing in the circuit with a resistance of 5 ohms. The voltage source works on the expression given, v = 10sin(30t) 

Solution: 

For calculating the value of the current Kirchhoff’s law can be used. 

∑ε(t) = 0

Applying this law to the circuit shown above, 

v + iR = 0 

10sin(30t) + i5 = 0 

i = -2sin(30t)

Problem 3: Find the expression for the current flowing in the circuit with a resistance of 20 ohms. The voltage source works on the expression given, v = 5sin(20t) 

Solution: 

For calculating the value of the current Kirchhoff’s law can be used. 

∑ε(t) = 0

Applying this law to the circuit shown above, 

v + iR = 0 

5sin(20t) + i(20) = 0 

i = -0.25sin(30t)

Problem 4: Average power dissipation in a circuit is given as 100W. The resistance of the circuit is 10 ohms. Find the peak value of the voltage in the circuit. 

Answer: 

Average power is given by, 

P = V²/R

Given: 

• V =? 
• R = 10 
• P = 100 

Plugging these values into the equation, 

P = V²/R

⇒ 100 = (V)² /10 

⇒ V = √1000

V = 10√10 V 

This is the RMS value of the voltage. 

Peak Value will be, 

V_peak = V_rms√2

⇒ V_peak = 10√20

⇒ V_peak = 20√5 V

FAQs on Alternating Current 

1. Define Alternating Current.

Alternating Current (AC) is an electric current that periodically reverses direction, changing polarity over time.

2. Who Invented the Alternating Current?

Alternating current (AC) electricity was developed by various scientists, with Nikola Tesla and George Westinghouse pioneering its practical use in the late 19th century.

3. What is an Alternating Current Generator?

An Alternating Current (AC) generator, often called an alternator, is a device that converts mechanical energy into AC electrical energy. It operates on the principle of electromagnetic induction.

4. What is Difference between AC and DC?

The main difference between Direct Current (DC) and Alternating Current (AC) lies in the direction of electron flow:

• DC: Electric charge flows in only one direction, from the positive (+) terminal to the negative (-) terminal.
• AC: Electric charge periodically reverses direction, constantly oscillating back and forth.

Why is AC more efficient than DC?

5. Which Source Produces Alternating Current?

Alternating Current is typically produced by AC generators or alternators. These generators convert mechanical energy into electrical energy using electromagnetic induction.

6. What Converts Alternating Current to Direct Current?

A device called a rectifier is used to convert Alternating Current (AC) to Direct Current (DC).

7. What is the Frequency of Alternating Current in India?

The frequency of Alternating Current (AC) in India is 50 Hz (Hertz). The power grid in India operates at this frequency, and most electrical appliances and devices in the country are designed to work with this standard frequency.