Alternating Current

What is Alternating Current?

Alternating current can be defined as a current that changes its magnitude and polarity at regular interval of time. It can also be defined as an electrical current which repeatedly changes or reverses its direction opposite to that of Direct Current or DC which always flows in a single direction as shown below.

AC and DC

From the graph, we can see that the charged particles in AC tend to start moving from zero. It increases to a maximum and then decreases back to zero completing one positive cycle. The particles then reverse their direction and reach the maximum in the opposite direction after which AC again returns to the original value completing a negative cycle. The same cycle is repeated again and again.

Alternating currents are also accompanied usually by alternating voltages. Besides, alternating current is also easily transformed from a higher voltage level to lower voltage level.

Alternating Current Production

Alternating current can be produced or generated by using devices that are known as alternators. However, alternating current can also be produced by different methods where many circuits are used. One of the most common or simple ways of generating AC is by using a basic single coil AC generator which consists of two-pole magnets and a single loop of wire having a rectangular shape.

In this setup, the AC generator follows Faraday’s principle of electromagnetic induction where it converts mechanical energy into electrical energy.

Application of Alternating Current

AC is the form of current that are mostly used in home appliances. Some of the examples of alternating current include audio signal, radio signal, etc. An alternating current has a wide advantage over DC as AC is able to transmit power over large distances without great loss of energy.

Alternating Current Waveform

Before we learn more about this topic, let us quickly understand a few key terms.

  • The time interval between a definite value of two successive cycles is the period.
  • The number of cycles or number of periods per second is frequency.
  • The maximum value in both directions is the amplitude.

Alternating Current Waveform

The normal waveform of AC in most of the circuits are sinusoidal in nature in which the positive half period corresponds with the positive direction of the current and vice-versa. In addition, a triangular or square wave can also be used to represent the alternating current waveform.

Audio amplifiers that deal with analogue voice or music signals produce irregular AC waves. Some electronic oscillators produce square or sawtooth waves.

Also Read: Differences Between AC and DC

Average Value of AC

Average value is usually defined as the average of the instantaneous values of alternating current over a complete cycle. The positive half cycle of asymmetrical waves such as a sinusoidal voltage or current waveform will be equal to the negative half cycle. Which implies that the average value after the completion of a full cycle is equal to zero.

Since, both the cycles do some work the average value is obtained by avoiding the signs. Therefore, the average value of alternating quantities of sinusoidal waves can be considered by taking the positive cycle only.

RMS Value of AC Wave

RMS value is defined as the square root of means of squares of instantaneous values. It can also be described as the amount of AC power that generates the same heating effect as an equivalent DC power.

Phasor Diagrams

The phasor diagram is used to determine the phase relationships between two or more sine waves propagating with the same frequency. Here, we use the terms “lead”, “lag” and also “in-phase”, “out-of-phase” to indicate the relation between one waveform with the other.

Phasor diagrams will be of the form:

Phasor Diagrams

AC Circuit Containing Resistance Only

The pure resistive AC circuit contains only pure resistance of R ohms. There will be no effect of inductance and capacitance in this circuit. The alternate current and voltage move along both the directions as backwards and forwards. Therefore, current and voltage follow a shape of sine.

In a purely resistive circuit, the power is dissipated by the resistors and phase of both voltage and current remains the same. Which means that the voltage and current reaches a maximum value at the same time.

AC Circuit Containing Resistance Only

Let the supply voltage be,

v = Vmsinωt ……(1)

The instantaneous value of current flowing through the given circuit is,

i = v / R = Vm / R sinωt ……(2)

From the equation (2), the value of current be maximum at t = 900, so sin t =1

Then, the instantaneous value of current will be,

i = Imsinωt ……(3)

So, by observing the equation (1) and (3), it is clear that there is no phase difference between the applied voltage and current flowing through the circuit. Meaning, phase angle between voltage and current is zero.

Hence, in a pure resistive ac circuit, the current is in phase with the voltage.

This can be expressed in a waveform as,

When current is in phase with the voltage

AC Circuit Containing Inductance Only

This type of circuit contains only inductance. There will not be any effect of resistance and capacitance in this circuit. Here, the current will lag behind the voltage by an angle of 900.

The circuit will be,

AC Circuit Containing Inductance Only

The inductor will reserves electrical energy in the magnetic field when current flows through it. When this current changes, the time-varying magnetic field causes emf which opposes the flow of current. This opposition to the flow of current is known as inductive reactance.

Let the voltage applied to the circuit be,

v = Vmsinωt ……(1)

The emf induced in the inductor will be,

E = -L x di / dt

This emf induced in a circuit is equal and opposite to applied voltage.

v = -e ……(2)

Putting the value of e in (2) we get,

v = (-L x di / dt)

Or

Vmsinωt = L x di / dt

Or

di = Vm / L sinω dt ……(3)

Integrating both sides, we get,

AC Circuit Containing Inductance Problem

Here,

Inductive reactance is XL = ωL

The value of current will be maximum if sin (ωt – π/2) = 1

Therefore,

Im = Vm / XL ……(5)

Apply the value of Im from (5) and put in (4)

We get,

i = Im sin (ωt – π / 2)

Which implies that the current in pure inductive ac circuits lags the voltage by 900.

This can be expressed in a waveform as,

Current in pure inductive ac circuits

If the voltage and current are at its peak value as a positive value, the power will also be positive. Similarly, if the voltage and current are at negative peak then the power will be negative. This is because of the phase difference between them.

AC Circuit Containing Capacitor Only

This type of circuit includes a pure capacitor only. It will not affect the properties of resistance and inductance. The capacitor will store electric power in electric field.this is known as capacitance.

The electric field is developed across the plates of the capacitor when a voltage is applied across the capacitor. Also, there will not be any current flows between them.

The circuit will be,

AC Circuit Containing Capacitor Only

As we know, a capacitor includes two insulating plates which are separated by a dielectric medium. Usually, capacitor works as a storage device and it gets charged if the supply is on and it gets discharged if the supply is off.

Let the voltage applied to the circuit be,

v = Vmsinωt ……(1)

Charge of the capacitor is,

q = Cv ……(2)

Then, current flow through the circuit will be,

i = d / dt X q

Substituting the value of q in the above equation we get,

i = d / dt (Cv) ……(3)

Now substitute the value of v in (3), we get,

AC Circuit Containing Capacitor Problem

Where XC = 1/C which is capacitive inductance.

The value of current will be maximum if sin(ωt + π/2) = 1.

Then, the maximum value of current,

Im = Vm / XC

Substituting the value of Im in (4) we get,

i = Im sin (ωt + π / 2)

Which implies that the current flowing through the capacitor leads the voltage by 900.

This can be expressed in a waveform as,

Current flowing through the capacitor leads the voltage by 90

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