Alternating Current
Alternating Voltage
A voltage that changes its magnitude and direction alternatively and achieves the same magnitude and direction again and again after a define interval of time is called
‘alternating voltage’.
V = Vm sin wt ………………(1)
ωWhen an alternating voltage is generated in coil the polarity of the terminal is changed after every T/2 time. Where, T is the time period of rotation of the coil generating the voltage. In Eq(1) ω is known as angular frequency of the alternating voltage. It is given by ω = 2π / T or ω = 2π ν ………………(2)
Where f is the frequency of the alternating voltage.
Alternating current:
A current which changes its magnitude and direction alternatively and achieves same value again and again after a definite interval of time is called alternating current or a.c.
I = Im sin (ωt + φ) ………………..(3)
Where Im is maximum Value or ‘peak value’ of current φ is the phase difference between alternating current and alternating voltage.
Case I
When φ = 0 current is said to be in the same phase as that of the voltage.
Case II
When φ = + ive current is leading over the voltage by angle φ or voltage lags behind the current by phase angle φ.
Case III
When φ = – ive current is lagging behind the voltage by phase angle φ or voltage is leading over the current by phase angle φ.
R.M.S. Value of current:
The current in an a.c. circuit is given by
I = Im sin ωt …………..……….(1)
If we determine the average value of current over the whole cycle is comes out to be zero.
So, we determine the r.m.s. value of current as:
“The square root of the average of square of the alternating current taken over the whole cycle is known as r.m.s. value of current”,
By eq (2)
Irms = 0.707 Im …………….(3)
Also by eq (2)
Im = √2 Irms ….………….(4)
The r.m.s value of current is considered effective value of current flowing in the a.c. circuit. It is also known as “ virtual current” flowing in the circuit. The a.c. ammeter measures the r.m.s. value of current.
Mean value of current
The average value of current in is known as the mean value of current.
PHASORS :
“ A phasor is a rotating vector whose magnitude is equal to the peak value of the quantity (voltage or current) and at any instant angle subtended by it with reference direction is equal to the phase of the quantity at that instant”.
The phasor rotates about the origin with constant angular speed w, and the component of it along the normal to the reference direction represents the instantaneous value of sinusoidally varying quantity (voltage and current) in a.c. circuit.
So, at any instant t the phasor for voltage makes an angle wt with the reference direction and the magnitude of the phasor is Vm. The magnitude of component of phasor in the direction normal to the reference direction is the instantaneous value of the quantity i.e. V = Vm sin ω t …..(1)
Similarly, at instant t, the phasor for current makes angle (ωt + f) to the reference line, so, the component of the phasor along normal to the reference line gives instantaneous value of current, which is given by I = Im sin (ωt + φ)
where Im is the magnitude of phasor for current.
