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# Formula for Calculating Wattless Current in AC

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Last updated date: 09th Aug 2024
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## An Insight to Wattless Current and it’s ongoings

The wattless current is a condition or exceptional instance of any AC circuit with just a capacitor or inductor. In any case, we can check the presence of wattless current by fulfilling the condition, which says the all-out power utilization should be equivalent to nothing.

The electric current in an AC circuit is said to be Wattless Current when the average power consumed or dissipated in the given electrical circuit is equal to zero or null. The current in an AC circuit is supposed to be Wattles Current when the normal power burned through in such a circuit relates to Zero. Such current is likewise called Idle Current. An AC circuit containing either capacitor or inductor current is said to wattles assuming that the normal power burned through in the circuit is zero.

The generation of wattless current essentially happens in purely inductive or capacitive electrical circuits only. In other words, the wattless current is produced only in an electrical circuit with a single capacitor or inductor. The reason behind this is that, in both inductive and capacitive electrical AC circuits, the voltage and current differ by a phase angle of 900 or π/2. We know that the average power depends upon the cosine component of the AC signal, which eventually becomes zero as the angle between them is ninety.

### Wattless Current

Let us have a look at the wattless current and the definition of inductor or capacitor is connected, then the total power consumption will be zero. The current flowing in such an electrical circuit in which the power consumption is zero is known as the wattles current. Such current is additionally called Idle Current. This essentially occurs in an inductive or capacitive circuit only. This is because of both inductive and capacitive circuits, the voltage and current vary by a staging point of 90.

The normal power relies on the cos part, which becomes zero as the point between them is ninety. Hypothetically, we can say that this peculiarity happens as it streams along the bearing of voltage or now and then totally against it, making the network zero. As network done methodologies is zero, the power likewise relates to zero, resulting in such a Current which is additionally cradled, Current. This essentially happens in an inductive or capacitive circuit only. In both inductive and capacitive circuits, the voltage and Current vary by a staging point of 90. The normal power relies on the cos part, which becomes zero as the point between them is ninety.

Hypothetically, we can say that this peculiarity happens as it streams along the bearing of voltage or now and then totally against it, making a network. As network methodology is zero, the power likewise relates to zero, resulting in a Wattless current.

Such electrical current will not consume any energy from the circuit. Theoretically, we can say that the generation of wattless current occurs as it flows along the direction of voltage or sometimes completely against it, causing it to zero. As networkers approach zero, the power will also start approaching zero, further which will end up resulting in a Wattless current.

### What is Wattless Current?

Then, what is the formula used for calculating wattless current in AC circuits? And what is wattless current? There is no particular formula for the wattless current. The wattless current is a condition or special case of any AC circuit with only a capacitor or inductor. But we can verify the presence of wattless current by satisfying the condition, which says the total power consumption must be equal to zero. This edition can be verified, which requires knowledge of the phase difference between the two sinusoidal waves. Let us have a look at the derivation of the wattless current with the help of the power equation.

### What are Wattless and Wattful current?

(I) The part of the current ( IRMS cos φ), which is in stage with the voltage, is called the active part. … The power devoured by this current VRMS IRMS cos φ. So it is otherwise called ‘Wattfull’ current.

What is the power factor of Wattless current?

The power factor is $cos\phi$ . For, wattless current, it's worth is $cos \frac{\phi}{2}$ = 0.

### Derivation:

The current in an electrical AC circuit is said to be Wattless Current when in any electrical circuit, to be more precisely in any electricity the l circuit consists of only an inductor or capacitor, and the total power consumption is zero. Wattless current is also known as Idle Current. Wattless current in any electrical AC circuit containing either a capacitor or inductor, then the current flowing in the circuit is said to wattles if the average power consumed circuit is zero.

The formula used for calculating the wattless current is given by:

P= V I cos φ……..(1)

Where,

V-The voltage applied to the circuit

I-The current flowing in the circuit

The φ-The phase difference between the voltage and current.

When the electrical circuit is consisting of only a capacitor or only an inductor then the phase the difference between the voltage and current is  π/2.Then equation (1) becomes:

P= V I cos  π/2

P=V I (0)P=0…..(2)

From equation (2), it is clear that the power consumed in an AC circuit with only an inductor or capacitor is zero. This condition is satisfied when the phase difference between the voltage and current is ninety. The current flowing in such a circuit is known as the wattless current.

Here, one important point to note is that when an AC circuit consists of only a capacitor it will lead by π/2 phase angle, and at the same time when an AC circuit consists of only an inductor it will lag by π/2 phase angle.

Examples

1. The RMS Current in an AC Circuit is 2A. If the Wattless Current is √3A,Then Calculate the Corresponding Power Factor of the Circuit?

Solution: Given, The Wattless Current is √3 A

We are asked to deduce the power factor of the circuit. We know that to attain the wattless current the phase angle between the current and voltage must be equal to π/2. Here we know that the given current is wattless current, but we want to find the power factor.

The Irms current can be split into two components as Irms cos φ and the Irms sinφ.The cosine component of the Terms is known as the power factor. Mathematically, we write:

Power factor = cos φP.

F = Cos φ

Now, the Irms sin φ component is perpendicular to the voltage, then the sine component of the Terms is the wattless current. Therefore we write:

Iw.l = I sin φ

√3 = 2 sin φ

sin φ = √3/2

φ = π/3 or 60 degree

Therefore, the power factor is given by:

P. F = Cos 60 = ½

Hence, the power factor in a given AC circuit is 0.5.

2. What is meant by the Wattless Current? Show that an Ideal Inductor does not consume any power in an AC Circuit.

Solution: The wattless current is defined as the current flowing in an electrical AC  circuit such that the circuit consists of either a capacitor or inductor, then the current flowing in the circuit is said to be wattless if the average power consumed in the circuit is zero. The formula used for calculating the wattless current or wattless current formula is given by

P= V I cos φ……..(1)

Where,

V = The voltage applied to the circuit

I = The current flowing in the circuit

The φ = The phase difference between the voltage and current

When the electrical circuit consists of only an ideal inductor then the phase difference between the voltage and Irms current is π/2. The Irms current can be split into two components as Irms cos ϕ and Irms sin ϕ. Both the components of the RMS currently play individual roles according to the need. For now, we assume that the cosine component of the RMS only contributes to the power, thus it is considered the only cosine as the wattless component of current. Then equation (1) becomes:

P= V I cos π/2

P=V I (0)

P=0…..(2)

From equation (2) it is clear that the power consumed in an AC circuit with only an ideal inductor is zero. Hence proved, that an ideal inductor does not consume any power in an AC circuit.

### Conclusion

Wattless current is otherwise called inactive current. If you do not practice the concepts on a daily basis, you’ll become like Wattless current. Acknowledge the need for a cumulative understanding and thorough reasoning. Therefore, the material is designed for easy understanding and fast learning. You can download the study material for free in the form of PDFs.

## FAQs on Formula for Calculating Wattless Current in AC

1. What is the meaning of the Wattless part of the current?

Wattless current is otherwise called inactive current. As we probably are aware, the power in a circuit is estimated in "watts" which is zero; for this situation, consequently, it is named wattless current. This mainly occurs in a simple inductive or capacitive circuit only. In both inductive and capacitive circuits, the voltage and current contrast by circuiting 90. As the average power relies on the cos part becomes zero, the point between them is ninety.

Hypothetically, we can say that this peculiarity happens as it streams along with the heading of voltage or some of the time, totally against it, making the network zero. As the network’s methodologies are zero, the power likewise compares to zero, resulting in a Wattless current.

2) Where is Wattless current utilized, and how can it be achieved in an AC circuit?

The wattless current is otherwise called the inactive current. The age of wattless flow occurs in simply inductive or capacitive electrical circuits, as it were. The wattless flow is created distinctly in an electrical circuit with a solitary capacitor or inductor.

In reality, you can't.

Current with no power requires voltage and current to be 90 degrees out of stage with one another. The state is challenging to accomplish despite the viable opposition in capacitors and inductors.

3) What is the power factor?

The power factor is how much the circuit devours real power (dynamic power) from the power (apparent power).

Suppose, that any circuit with a 0.8 power factor and devouring 100kVA then the real power, for example; dynamic power, can be discovered by 1000.8=80kW.

In this way, the 0.8 power factor implies that 80% of aggregate (apparent) power is utilized by the circuit, such as dynamic power.

Furthermore, numerically, it is characterized as the cosine of points among voltage and current. In AC circuits, there will be a stage distinction (phi) between voltage and current. The cosine of this point is phi and as a power factor. Assuming that the circuit is inductive, the current will slack voltage; then, at that point, the power factor is supposed to slack. Then again, if the circuit is capacitive, which currently leads to the voltage, then, at that point, the power factor is supposed to be driving.

In straightforward words, in a solitary stage AC circuits,

$P = V \times I \times cos \phi$

Where $cos\phi$ is called a power factor.

4) How might you acquire a wattless current in an AC circuit?

Through an unadulterated inductive or capacitive circuit. Wattless current is seen when the normal power devoured by the circuit is equivalent to nothing. This can be accomplished when the circuit has just responsive parts like Capacitor or Inductor. This is because the stage distinction between current and voltage is 90 degrees for both capacitor and inductor, and the 'Cos' factor chooses the power. So 'Cos 90' is Zero, and thus the power burned-through will be equivalent to Zero, which is called Wattless current.

5) Differentiate between the AC and DC voltage?

Both powerful power and give out power. If you use a cycle siphon or a water hand siphon, you give the energy in two ways which are exchanged all over the place—any uncertainty in it. The progression of air or water is just one way, however irregular. Air from a fan or water from a tap is persistent and one way. So we use energies of the two assortments. These exist with power, moreover. All electronic hardware utilizes DC direct current, which is drawn from house divider attachment which gives AC and changed over into DC before being taken care of to the gear inside. For PDAs, the change happens outside the telephone with a thing which we call a charger. Some hardware such as fans, radiators, coolers run straight by AC.