Power in Alternating Current: AC Circuit and The Power Factor

This particular article talks about the two different kinds of current, Alternating Current and Direct Current, focusing mainly on Alternating Currents. Stating the characteristics of Alternating currents, their causes, and their advantages also gives an idea of power consumed in an AC circuit, the power factor, and the important formulae of the same. Pertaining to the direction of current flowing through the circuit, it is classified into two types namely, being- 1. Alternating Current (AC) and 2. Direct Current (DC). When an electric current reverses direction periodically while traveling through an electric circuit it is known as the Alternating Current while the current flowing only in one direction is referred to as the Direct Current.

Key Terms: AC Current, Causes of AC, Alternating voltage, Power factor, Alternating current, AC circuit, Dc Current, Magnitude

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Characteristics of Alternating Current (A/c) 

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• Alternating Current can be defined as an electric current that reverses its direction in periodic intervals and changes its magnitude continuously with time.
• The value of such a current will oscillate from a minimum to a maximum value.
• The direction of the current shall be either clockwise and anticlockwise and the same shall keep on repeating.
• In the case of Alternating Current, the current is changing its magnitude at every instance of time.
• The frequency of the alternating current can be measured by measuring how fast the electrons change their directions. For example- if the frequency is taken to be 20Hz then it can be said that the electrons are moving back and forth almost 20 times in a time period of 1 second.
• Just like DC voltage gives rise to DC current, similarly, AC voltage gives rise to A/c current.
• Alternating current is expressed by using the following expression- I = I_msinωt

Alternating Current

where I_m = maximum or peak value of A/c

• An alternating voltage is by using the following expression- V = V_msinωt

Where V_m = Peak value of voltage

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Causes of alternating current

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When a rotating magnet is considered in place of a steady magnetic field causing both the poles of the magnet to change as a result of which the direction of the electrons also gets reversed. This results in oscillation of electrons which in turn gives rise to current and this itself are known as alternating current. 

Alternating Current

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Advantage of Alternating Current

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The primary advantage of alternating current is that the AC voltages can be easily switched from higher to lower voltage levels and vice versa. As a result of this quality, high voltage power from power stations can be reduced to a safe voltage for domestic use. Only alternating current can flow through inductors and capacitors. By using the same within the alternating current circuits, the flow of electricity can be turned. This also helps in the tuning of radio stations. Owing to all these reasons, AC electricity is the most preferred for home gadgets and appliances.

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Power consumed in an A/C circuit

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An electric circuit produces power which is mentioned with the help of the expression, P=IV, where I= indicates the current flowing through the circuit and V=indicates the voltage across it.

AC circuits always offer reactance which is why there are two components of power due to the a) magnetic field and b) electric field. The average power absorbed by the circuit becomes the sum of the power stored and the same is returned through a completed cycle. Therefore, the average power consumed by the circuit will be immediate power within one cycle.

Since the current flowing through the circuit and voltage are dependent on time, the immediate power is also dependant on time. It is expressed as

p (t) = I (t)* v(t); where time is denoted by t.

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Power Factor

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• The power factor of an alternating current is defined as the ratio of the true power flowing through the circuit towards the evident power present in the circuit.
• It usually ranges from the intervals of -1 to 1 and is dimensionless.

It is denoted by the expression as follows-

Power Factor =True Power/Evident Power;

or, cos ø= R/Z

where R= resistance in the circuit and Z= hindrance in the circuit.

For a purely inductive or capacitive circuit, it is 0 and for a purely resistive circuit, it is taken to be 1.

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Important Explanations and Formulas

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• The average power of an alternating current circuit can be calculated by calculating the immediate power of the circuit. Therefore, in an AC circuit, the average power dissipation can be calculated by-

Power factor = \(\frac{Active power}{Apparent power}\)

= \(\frac{VIcos\theta}{VI}\)

= cosθ

P_av = ₀∫^T VI dt / ₀ ∫^T dt

Thus, the immediate e.m.f and the current in an AC circuit are are given by:

V= V₀ sin ωt

I= I₀ sin (ωt – ø)

• In a series LCR circuit, the following is show-

P_av =V_rms I_rms cøs

where, V0 and I0 are taken to be the peak values of e.m.f along with current and ω = 2π/t t= period of the alternating current and Vrms and Irms is known as the evident or virtual power.

• If ø=0 then,

P_av = I²_rms R

Hence, power dissipation takes place only in the resistor of an AC circuit.

• For a series LCR circuit at resonance, a completely resistive circuit is given as:

&Ø= 0^o  and the same is represented as,

P_av = V_rms I_rms

Thus, for a completely indicative or capacitive circuit, ø= 90^o

Resulting in, P_av = 0

• Power increases when an AC circuit contains the resistor. The power of an AC circuit decreases when a capacitor or an indicator is included to the series coupled with a resistor.

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Things to Remember

• Alternating Current can be defined as an electric current that reverses its direction in periodic intervals and changes its magnitude continuously with time.
• Alternating current is expressed by using the following expression- I = I_msinωt where I_m= maximum or peak value of A/c. 
• The primary advantage of alternating current is that the AC voltages can be easily switched from higher to lower voltage levels and vice versa.
• The flow of electricity can be turned in the alternating current circuits which helps in the tuning of radio stations.
• An electric circuit produces power which is mentioned with the help of the expression, P=IV, where I= indicates the current flowing through the circuit and V=indicates the voltage across it.
• The power factor of an alternating current is defined as the ratio of the true power flowing through the circuit towards the evident power present in the circuit.
• It usually ranges from the intervals of -1 to 1 and is dimensionless.
• Power increases when an AC circuit contains the resistor. The power of an AC circuit decreases when a capacitor or an indicator is included to the series coupled with a resistor.

Also Read:

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Previous Year Questions 

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