Power in an A.C. Circuit

Alternating Current 

A circuit can be divided into two groups based on the direction of current flow. Electricity is divided into two types: alternating current and direct current. When an electric current changes direction frequently while going across an electric circuit, it is known as Alternating Current (AC). When current solely flows in one direction, it is known as “direct current” (DC).

Advantages of Alternating Current

Alternating current has several advantages, including the ability to transition between higher and lower voltages with ease. As a result, high-voltage output from power plants can be decreased to a level that is more manageable for domestic usage. Only alternating currents can be employed with capacitors and inductors. Using them in alternating current circuits can reverse the flow of power. This function assists in the discovery of radio stations. For all of these reasons, alternating current energy is almost extensively used in household appliances (AC).

Alternating current circuits, on the other hand, have a constant electromotive force and a constant current. Because power is equal to the product of voltage and time, this is the main reason why we can’t calculate the power for it. The instantaneous output power of a circuit can be used to calculate its average power.

Consumption of Power in an AC circuit

P= I V is the formula for calculating the power in an electric circuit.

Where I represents the current in the circuit and V represents the voltage across it.

Because of the magnetic field and the electric field, there are always two power components in AC circuits. The total power stored and returned over the duration of a single cycle is the circuit’s average power consumption. As a result, the circuit’s average power consumption will be the same as the power consumed during a single operation cycle.

Because the current passing through the circuit and the voltage are both time-dependent, the instantaneous power is as well. It is provided by,

 P (t) = I (t) x v (t).

 Consider the LCR circuit, which has a voltage V supplied to it. The voltage V is calculated as follows:

 V = Vm× sinωt

 The current in this case is written by:

 I = Im × sin(ωt+Φ )

Where,  Vm – amplitude of Voltage

Im –  Amplitude of current

ω- Angular frequency.

Φ – Phase constant

Current amplitude is given as Im = Vm/Z

Where Z is the impedance of the circuit and it is calculated by

Z =√[ (XL−XC)2+R2]

Here XL is the impedance of the inductor and XC is the impedance of the capacitor.

tanΦ = (XL−XC)/R

Or,  Φ = tan-1 (XL− XL)/R

 All the above equations can be used to find the consumption of power in an AC circuit,

 We know, P = IV

P = (Vm sin⍵t) × (Im sin(⍵t + Φ))

Power Factor

The ratio of the genuine power flowing through the circuit to the apparent power existing in the circuit is known as the power factor of an alternating current.

It normally falls between -1 and 1 and is dimensionless.

Power Factor = True Power/ Apparent power

Also, cosΦ = R/Z

R- resistance in the circuit

Z- impedance of the circuit.

Important points

• Divide the RMS voltage by the impedance to get Ohm’s law for the RMS value of an alternating current.
• The phase angle affects the average power delivered to an LCR circuit.

Conclusion 

When current and voltage are multiplied, the average ac power is calculated. RMS voltage is divided by impedance in order to find Ohm’s law for the RMS AC. In an ac circuit, the source voltage and current have a phase angle that can be determined by dividing the resistance by the impedance.