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Alternating Current
Chapter Cover: Section A - Average and RMS value of Alternating Current
1. ALTERNATING CURRENT
Until now, we have studied only circuits with direct current (dc) which flows only in one direction (as shown in figure I and II). The primary source of emf in such circuit is a battery. When a resistance is connected across the terminals of the battery, a current is established in the circuits, which flows in a unique direction from the positive terminal to the Negative terminal via the external resistance.
Fig-I
Fig-II
But most of the electric power generated and used in the world is in the form of alternating current (ac), the magnitude of which changes continuously with time and direction is reversed periodically (as shown in figure III & IV)and it is given by
i=i_{0}sin (ωt + ϕ)
Here i is instantaneous value of current i.e., the magnitude of current at any instant of time and i_{0} is the maximum value of current which is called peak current amplitude and the current repeats its value after each time interval T = as shown in figure, This time interval is called the time of period and ω is angular frequency which is equal to 2π times of frequency f.
The current is positive for half the time period and negative for remaining half period. It means that the direction of current is reversed after each half time period. The frequency of ac in India is 50 Hz.
An alternating voltage is given by
V=V_{0} sin (ωt +ϕ)
It also varies alternatively as shown in the figure (b), where V is instantaneous voltage and V_{0} is peak voltage. It is produced by ac generator also called as ac dynamo
Ac Circuit: An ac circuit consists of circuit element i.e., resistor, capacitor, inductor or any combination of these and a generator that provides the alternating current as shown in figure. The ac source is represented by symbol _{} in the circuit.
2. AVERAGE AND RMS VALUE OF ALTERNATING CURRENT
2.1 Average current (mean current) As we know an alternating current is given by
i= i_{0} sin (ωt + ϕ) …… (1)
The mean or the average value of ac over any time T is given by
i_{avg = }
Using equation (1)
i_{avg }=
In one complete cycle, the average current
i_{avg}=
=
=
Since ac is positive during the first half cycle and negative during the other half cycle so i_{avg }will be zero for long time also. Hence the dc instrument will indicate zero deflection when connected to a branch carrying ac current. So it defined for either positive half cycle or negative half cycle.
i_{avg = }
Electromagnetic Induction
Chapter Cover: Section A - Flux, Faraday’s law, Lenz’s law
1. MAGNETIC FLUX
Note
2. FARADAY’S LAE OF ELECTROMAGENTIC INDUCTION
…. (iii)
3. LENZ’S LAW
4. CALCULATION OF INDUCED EMF
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