- Introduction
- |
- Alternating current and Alternating EMF
- |
- Average or mean current
- |
- Root Mean square value of AC
- |
- Phasor diagram
- |
- A.C through pure resistor
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- A.C through pure inductor
- |
- AC through pure capacitor
- |
- Circuit containing inductance and resistance in series
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- Circuit containing capacitance and resistance in series
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- LCR series circuit

- We know that time average value of AC over one cycle is zero and it can be proved easily

- Instantaneous current I and time average of AC over half cycle could be positive for one half cycle and negative for another half cycle but quantity i
^{2}would always remain positive

- So time average of quantity i
^{2}is

This is known as the mean square current

- The square root of mean square current is called root mean square current or rms current.

Thus,

thus ,the rms value of AC is .707i_{0}of the peak value of alternating current

- Similarly rms value of alternating voltage or emf is

- If we allow the AC current represented by i=i
_{0}sin(ωt+φ) to pass through a resistor of resistance R,the power dissipated due to flow of current would be

P=i^{2}R

- Since magnitude of current changes with time ,the power dissipation in circuit also changes

- The average Power dissipated over one complete current cycle would be

If we pass direct current of magnitude i_{rms}through the resistor ,the power dissipate or rate of production of heat in this case would be

P=(i_{rms})^{2}R

- Thus rms value of AC is that value of steady current which would dissipate the same amount of power in a given resistance in a given tine as would gave been dissipated by alternating current

- This is why rms value of AC is also known as virtual value of current

- Phasor diagrams are diagram representing alternating current and voltage of same frequency as vectors or phasors with the phase angle between them

- Phasors are the arrows rotating in the anti-clockwise direction i.e. they are rotating vectors but they represents scalar quantities

- Thus a sinusoidal alternating current and voltage can be represented by anticlockwise rotating vectors if they satisfy following conditions
- Length of the vector must be equal to the peak value of alternating voltage or current
- Vector representing alternating current and voltage would be at horizontal position at the instant when alternating quantity is zero
- In certain circuits when current reaches its maximum value after emf becomes maximum then current is said to lag behind emf

- When current reaches its maximum value before emf reaches its maximum then current is said to lead the emf

- Figure below shows the current lagging behind the emf by 90
^{0}

- Figure below shows the circuit containing alternating voltage source V=V
_{0}sinω connected to a resistor of resistance R

- Let at any instant of time ,i is the current in the circuit ,then from Kirchhoff’s loop rule

V_{0}sinωtRi

or

i=(V_{0}/R)sinωt

=i_{0}sinωt ----(8)

Where,

i_{0}=V_{0}/R ----(9)

- From instantaneous values of alternating voltage and current ,we can conclude that in pure resistor ,the current is always in phase with applied voltage

- Their relationship is graphically represented as

Class 12 Maths Class 12 Physics

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