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Power of Alternating Current is the ratio of the true power flowing through the circuit to the apparent power present in the circuit. In alternating current circuit, electromotive force and current change with respect to time. Thus, its power cannot be calculated as it will fall equivalent to product of voltage and time. Average Power of an Alternating Current circuit can be calculated by calculating the instantaneous power of the circuit.
Read More: Difference between Earth and Neutral
Key Terms: Alternating Current, Direct Current, AC, DC, Electricity, Circuit, Power Factor, Force, Electric circuit
Definition of Alternating Current
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Alternating Current or AC can be defined as the current that varies with time like a sine function. Its value oscillates between a maximum value and a minimum value. The magnitude of AC keeps changing at every instant of time. The direction of AC is clockwise and anticlockwise and this keeps on repeating. Therefore, in simple words, we can also say that when an electric current reverses its direction periodically during its flow through an electric circuit, it is called AC or Alternating Current.
Alternating Current
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Frequency and Expression of Alternating Current
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The frequency of an AC can be defined by how fast the electrons change their directions. For example, an AC with a frequency of 20 Hz means the electrons are moving backward and forward 20 times in 1 second.
Alternating Current is expressed asI = Im sinωt
(Where Im is the Maximum or Peak Value of AC)
Alternate Voltage is expressed as V = Vm sinωt
(Where Vm is the Maximum or Peak Value of the Voltage)
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Causes for Alternating Current
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An Alternating Current is caused by an electric generator. An electric generator consisting of a loop of wire and a magnet rotates in the magnetic field produced by the magnet. With the rotation of the wire, a force is produced by the changing strength of the magnetic field which drives the electric charge around the wire. Initially, this force generates an electric current along the wire that travels in one direction. As the loop of the wire rotates 180 degrees, the direction, and flow of the current change. This changing direction of the current after repeated 180 degrees reversal generates an alternating current. The electric generator also has slip rings besides having a magnet and a wire. These slip rings make sure that the ends of the wire always remain connected to the same side of the electric circuit. This ensures that the direction of the current changes after every half revolution along the wire.
Causes for Alternating Current
Differences between Alternating Current and Direct Current
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There are some primary distinguishing points between Alternating Current and Direct Current. These are mentioned in the table below:
| Alternating Current (AC) | Direct Current (DC) |
|---|---|
| The direction of the electric flow along the wire switches back and forth at regular intervals in the electric circuit. | The direction of the electric flow along the wire remains steady and in one direction only in the electric circuit. |
| The voltage in an AC circuit keeps reversing periodically as the current changes its direction. | The voltage in a DC circuit remains constant as the current does not change its direction. |
| The frequency of AC is 50 Hz to 60 Hz based on the country. | The frequency of DC is zero. |
| Generally, AC is of sinusoidal type. Other variations include triangular or square trapezoidal types. | The DC current is generally of a pure and pulsating form. |
| AC is safer to transfer over long distances and for maintaining electric power. | As compared to AC, DC cannot travel over very long distances, as it keeps losing its electric power. |
| It is generated mostly by AC generators. | It is generated by either battery, photovoltaic cell, or electrochemical cell. |
| Electric Motors, AC Generator, and Mains, Refrigerators, Dishwashers, Washing Machines, various Home Appliances, etc. | Cell Phones, Battery, Flashlights, Flat-Screen TVs, LilyPad, Hybrid and Electric Vehicles, etc. |
Alternating Current and Direct Current
Advantages of Alternating Current
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Alternating Current is advantageous because it is relatively cheap to change the voltage of an AC. It can be easily transformed from higher voltage levels to lower voltage levels and vice-versa. Besides, the inevitable loss of energy that takes place during carrying current over long distances is quite less with alternating current. As a result, they are used for domestic appliances. High voltage power from power stations is easily transformed to lower and safer voltage levels for domestic use without the worry of short-circuiting or high expenses on wasted energy. The flow of electricity can be turned simply by using AC within alternating current circuits.
Power of Alternating Current
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In an alternating current circuit, there is a continuous change in electromotive force and the current with respect to time. As a result, its power cannot be calculated since power is equal to the product of time and voltage. The average power can be calculated by finding the instantaneous power of the AC circuit. The average power dissipation can be calculated by the following formula:
Pa=∫T0 VI dt / ∫T0 dt
The formula for instantaneous e.m.f. and the current in the AC circuit is:
V = V0sinωt
I = I0sin (ωt − \(\phi\))
Power Factor
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Power in an AC circuit increases when it consists of a resistor. The power similarly decreases when the circuit is connected in series to the circuit by an inductor or a capacitor. The average power of an AC circuit is also called the true power of an electrical circuit. This is known as the Power Factor of the circuit.
Hence, the Power Factor of an electrical AC circuit can be defined by the ratio of true power dissipation to the apparent power dissipation within the circuit.
Power Consumed in an Alternating Current Circuit
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The power produced by an electric circuit is given by the expression P = I V (where I stands for the current flowing in the circuit and V stands for the voltage).
An Alternating Current circuit offers reactance. There are two components of power- one because of the magnetic fields and another because of the electric field produced. The average power that is absorbed by the AC circuit is the sum of the power stored and returned through one complete cycle. Therefore, the average power consumed by the AC circuit is an instantaneous power within one cycle.
Since the current flowing through the AC circuit and the voltage across it is dependent on time, the instantaneous power is also dependent on time ‘t’. The formula for this is:
p (t) = l (t) x v (t)
Things to Remember
- An electric current that reverses its direction periodically during its flow through an electric circuit, is called AC or Alternating Current.
- In Alternating Current, electrons keep switching their direction back and forth.
- AC is expressed by the formula I = Im sinωt and Alternate Voltage is expressed by V = Vm sinωt .
- AC is mainly produced by AC generators, which consist of a magnet and a wire.
- Alternating Current is used in various home appliances since it is comparatively easier to handle than Direct Current.
- The biggest advantage of AC is that it can travel over long distances as electron loss is very less in AC. This also reduces any expense over the inevitable loss of energy caused during travelling over distances.
- An electrical circuit that is sourced by an Alternating current or voltage is called an AC circuit or alternating current circuit.
- The average power in an AC circuit can be calculated by calculating the instantaneous power produced by it.
- Power Factor of an AC circuit is the ratio of true power dissipation to the apparent power dissipation within the circuit.
Previous Year Questions
- In the circuit shown, the symbols have their usual meanings… [BITSAT 2018]
- An electrical cable having a resistance of… [WBJEE 2009]
- A coil of inductance 8.4 mH and resistance… [JEE Advanced 1999]
- A coil of resistance 10Ω and inductance… [VITEEE 2011]
- For a coil having L = 2 mH, current flow through it is… [NEET 2001]
- A direct current of 5A is superposed on an alternating current… [NEET 2015]
- A resistance wire of 72Ω is connected across 120 V dc source… [COMEDK UGET]
- A 220volt input is supplied to a transformer… [NEET 2010]
- A 40μF capacitor is connected to a 200V, 50Hz ac supply… [NEET 2020]
- A circuit when connected to an AC source of 12V gives a current of… [NEET 2019]
- A coil has resistance 30 ohm and inductive reactance… [NEET 2011]
- A coil is self-inductance L is connected in series with a bulb… [NEET 2013]
- A condenser of capacity C is charged to a potential difference… [NEET 2010]
- A series LCR circuit is connected to an ac voltage source… [NEET 2020]
- A transformer having efficiency of 90% is working on… [NEET 2014]
- An ac voltage is applied to a resistance R and an inductor… [NEET 2011]
- An inductor 20mH, a capacitor 50μF and a resistor… [NEET 2016]
- In the given circuit the reading of voltmeter V1 and V2 are 300 volts each… [NEET 2010]
- Which of the following combinations should be selected for… [NEET 2016]
- In an A.C. circuit, V and I are given by V=150 sin… [KCET 2011]
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Sample Questions
Ques. What is the simplest way to recognize AC voltage? (1 mark)
Ans. Generally, an AC current is composed of sinusoidal waves. As a result, an AC Voltage varies sinusoidally, which is the simplest way to recognize it.
Ques. What is the significance of ‘Alternating’ in Alternating Current or AC? (1 mark)
Ans. ‘Alternating’ in Alternating Current refers to the continuous reversal of electric charge after every half cycle direction of the flow of the electric current generated in an AC generator. This causes a repeated change in the direction of the current produced, which is rightfully called ‘Alternating’ Current.
Ques. What are the disadvantages of Alternating Current? (1 mark)
Ans. Alternating Current usually has a very high peak value, which can be dangerous if contacted. As a result, good insulation is absolutely required. Unlike Direct current that produces a repelling shock effect, Alternating current is transmitted from the surface of the conductor and attracts contact.
Ques. Is Alternating Current disadvantageous over Direct Current? (1 mark)
Ans. Alternating Current is often considered bad when compared to Direct current. This is because unlike DC, which has a stable magnitude and direction, AC constantly fluctuates in magnitude and changes direction. As a result, the root mean squared value of AC is much higher than the original value. Ac current also produces a direct impact on our heart as it carries a high electric frequency. It can also reduce our skin’s resistance which may cause a large current to enter our body.
Ques. Can we convert Alternating Current to Direct Current? (1 mark)
Ans. Yes, Alternating Current can be converted into Direct Current by using a device called the Rectifier. It periodically reverses the flow and direction and helps to straighten AC into DC.
Ques. How many types of power can be defined from an AC circuit? (1 mark)
Ans. Three types of power can be defined from an AC circuit- Instantaneous Power, Average Power and Apparent Power. The power dissipated in an AC circuit can be determined by the formula P = I V where I is the current flowing through the circuit and V is the voltage across it.
Ques. What is Virtual Power in an AC circuit? (1 mark)
Ans. Apparent Power is also known as Virtual Power in an AC circuit, whereas the Average Factor is also called the True Power.
Ques. What is the measuring unit of the Power Factor in an AC circuit? (1 mark)
Ans. The power factor of an AC circuit is the ratio between the resistance and impedance of the circuit. Since both are resistance quantities, the ratio between them is 1, and the power factor is, therefore, a unitless and dimensionless quantity.
Ques. What is the power factor in a purely resistive AC circuit? (1 mark)
Ans. The power factor in a purely resistive AC circuit is 1 since the reactive power in the circuit equals to zero. The formula for this is Φ = 0 → Power factor (cos 0) = 1
Ques. A wire of resistance R is connected in series with an inductor of reactance ωL. Find the quality factor of the RL circuit. (4 Marks) [AIPMT 2000]
Ans. We define the quality factor of the circuit as follows:
Quality factor Q =
But the total energy stored in circuit
So, loss in energy per cycle
Hence, the quality factor
=
Ques. Why is the use of A.C. voltage preferred over D.C. voltage? Give two reasons. (2 Marks) [All India 2013]
Ans. A.C. Voltage is preferred over d.c. voltage because of the following reasons:
- It can be stepped up or stepped down by a transformer.
- Carrying losses are much less.
Ques. Mention the two characteristic properties of the material suitable for making the core of a transformer. (3 Marks) [All India 2012]
Ans. Characteristic properties of material suitable for the core of a transformer :
- It should have high permeability
- It should have low hysteresis loss.
- It should have low coercivity/retentivity.
- It should have high resistivity. (Any two)
Ques. Why it is not possible to have electrolysis by A.C? (2 Marks)
Ans. An alternating current reverses its direction after each half cycle. Therefore on passing A.C through a solution, the motion of the positive and negative ions becomes vibratory.So ions are not separated. So that is the reason electrolysis does not happen in A.C. Also, Batteries cannot be charged through A.C for this reason only.
Ques. An Inductor L of inductance XL is connected in series with bulb B and an ac source. How would the brightness of the bulb change when
(a) the number of turns In the Inductor Is reduced,
(b) an Iron rod Is Inserted Into the Inductor and
(c) a capacitor of reactance XC = XL
Is Inserted in series In the circuit. Justify your answer In each case. (3 Marks) [CBSE Delhi 2015]
Ans. (a) When the number of turns of the inductor is reduced it decreases the inductance of the inductor as (L ∝ n2) where n is the number of turns. This in turn decreases the inductive reactance XL which increases the current in the circuit and hence the brightness of the bulb decreases.
(b) When an iron rod is inserted in the inductor, it increases the inductive reactance, which in turn decreases the current and hence the brightness of the bulb.
(c) When XL = XC, the circuit acts as a resistive circuit, i.e. the impedance becomes minimum and maximum current flows. This makes the bulb glow more brightly.
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