In an AC circuit with only a pure inductor, why is the current called "wattless," and what is the power factor? Explain why no real power is consumed in this circuit.

The current in a purely inductive circuit is called "wattless" because the 90° phase difference between voltage and current causes zero real power consumption. The power factor is zero, meaning no energy is converted to work, only reactive power is exchanged.

What are the limitations of wattless current?

Wattless current means that no energy is converted into useful work, such as heating, lighting, or mechanical motion. In practical terms, this is inefficient because the energy provided by the source is not being utilized for any productive purpose.

How can wattless current be obtained in an AC circuit?

To obtain wattless current in an AC circuit, you can use either a purely inductive circuit or a purely capacitive circuit. In both cases, the current and voltage are out of phase by 90 degrees, resulting in zero real power consumption. The current in these circuits is called wattless because it does not perform any useful work.

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Wattless Current

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Wattless Current

Wattless current, also known as idle current, is the current in an AC circuit that does not contribute to real power. It flows between the source and reactive components (inductors or capacitors) but does not perform any useful work, as the average power over a full cycle is zero.Wattless current does not dissipate energy in the form of heat, as it only causes a temporary energy shift between the source and reactive components.

1.0Definition Of Wattless Current

It is the component of the circuit current that results in zero power consumption in the circuit.

2.0Formula And Diagram of Wattless Current

$P " = V_{r m s} (I_{r m s} S in ϕ) C os \frac{π}{2} = 0$

P''=0

3.0Explanation of Wattless Current

The average power consumed over a complete cycle is given as, $P = V_{r m s} I_{r m s} C os ϕ$
$ϕ$ is the phase angle between $V_{r m s} an d I_{r m s}$ . Resolving $I_{r m s}$ into two components,

$I_{r m s} C os ϕ$ along $V_{r m s}$
$I_{r m s} s in ϕ$ perpendicular to $V_{r m s}$

Avg. power consumed in the circuit due to component $I_{r m s}$ Cos $ϕ$ of current $I_{r m s}$ is given as,

$P^{'} = V_{r m s} (I_{r m s} cos ϕ) C os 0^{o}$ (ஃ Phase angle between Vrms and $I_{r m s} C os ϕ$ is zero)

$P " = V_{r m s} I_{r m s} C os ϕ$

Avg. power consumed in the circuit due to component $I_{r m s} S in ϕ$ of current Irms is given as,

$P " = V_{r m s} (I_{r m s} S in ϕ) C os \frac{π}{2} = 0$

P''=0 $\Rightarrow$ Wattless Current

$\Rightarrow$ The avg. power consumed in the circuit due to $I_{r m s} S in ϕ$ The component of current is zero. This component of current is called Wattless Current.

Note: Power is consumed due to $(I_{r m s} C os ϕ)$ component so it is known as wattful component.

4.0Sample Question on Wattless Current

Q-1.The instantaneous current and voltage of an alternating current circuit is given by $I = (10 S in 314 t) A$ and $V = 50 S in (314 t + \frac{π}{2}) V$ . What is the power dissipation in the circuit?

Solution:

$ϕ = \frac{π}{2}$

Power Dissipation= $\frac{1}{2} V_{0} I_{0} C os ϕ$

$\frac{1}{2} V_{0} I_{0} C os \frac{π}{2} = 0$

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Wattless Current

Wattless current, also known as idle current, is the current in an AC circuit that does not contribute to real power. It flows between the source and reactive components (inductors or capacitors) but does not perform any useful work, as the average power over a full cycle is zero.Wattless current does not dissipate energy in the form of heat, as it only causes a temporary energy shift between the source and reactive components.

1.0Definition Of Wattless Current

It is the component of the circuit current that results in zero power consumption in the circuit.

2.0Formula And Diagram of Wattless Current

$P " = V_{r m s} (I_{r m s} S in ϕ) C os \frac{π}{2} = 0$

P''=0

3.0Explanation of Wattless Current

The average power consumed over a complete cycle is given as, $P = V_{r m s} I_{r m s} C os ϕ$
$ϕ$ is the phase angle between $V_{r m s} an d I_{r m s}$ . Resolving $I_{r m s}$ into two components,

$I_{r m s} C os ϕ$ along $V_{r m s}$
$I_{r m s} s in ϕ$ perpendicular to $V_{r m s}$

Avg. power consumed in the circuit due to component $I_{r m s}$ Cos $ϕ$ of current $I_{r m s}$ is given as,

$P^{'} = V_{r m s} (I_{r m s} cos ϕ) C os 0^{o}$ (ஃ Phase angle between Vrms and $I_{r m s} C os ϕ$ is zero)

$P " = V_{r m s} I_{r m s} C os ϕ$

Avg. power consumed in the circuit due to component $I_{r m s} S in ϕ$ of current Irms is given as,

$P " = V_{r m s} (I_{r m s} S in ϕ) C os \frac{π}{2} = 0$

P''=0 $\Rightarrow$ Wattless Current

$\Rightarrow$ The avg. power consumed in the circuit due to $I_{r m s} S in ϕ$ The component of current is zero. This component of current is called Wattless Current.

Note: Power is consumed due to $(I_{r m s} C os ϕ)$ component so it is known as wattful component.

4.0Sample Question on Wattless Current

Q-1.The instantaneous current and voltage of an alternating current circuit is given by $I = (10 S in 314 t) A$ and $V = 50 S in (314 t + \frac{π}{2}) V$ . What is the power dissipation in the circuit?

Solution:

$ϕ = \frac{π}{2}$

Power Dissipation= $\frac{1}{2} V_{0} I_{0} C os ϕ$

$\frac{1}{2} V_{0} I_{0} C os \frac{π}{2} = 0$

Frequently Asked Questions

In an AC circuit with only a pure inductor, why is the current called "wattless," and what is the power factor? Explain why no real power is consumed in this circuit.

Define Wattless Current?

What are the limitations of wattless current?

How can wattless current be obtained in an AC circuit?

Join ALLEN!

Wattless Current

1.0Definition Of Wattless Current

2.0Formula And Diagram of Wattless Current

3.0Explanation of Wattless Current

4.0Sample Question on Wattless Current

Table of Contents

Frequently Asked Questions

In an AC circuit with only a pure inductor, why is the current called "wattless," and what is the power factor? Explain why no real power is consumed in this circuit.

Define Wattless Current?

What are the limitations of wattless current?

How can wattless current be obtained in an AC circuit?

Join ALLEN!

Wattless Current

1.0Definition Of Wattless Current

2.0Formula And Diagram of Wattless Current

3.0Explanation of Wattless Current

4.0Sample Question on Wattless Current

Table of Contents