Alternating current
Advantage of AC over DC
1.AC board ki jis can be easily and efficiently converted from one voltage to other
2.Electrical energy due to AC can be transmitted economically over long distances.
AC voltage applied to a resistor
i =im sinwt
v =vmsinwt
1.im=vm/R
2. Instantaneous power=im2 R sin2wt
3. Average power=im2/2R
4.irms=im/√2
vrms=vm/√2
5. The current is in phase with the voltage
AC voltage applied to an inductor
i. = - im coswt
v. = vmsinwt
1. im=vm/XL. (XL=Lw,the inductive reactance)
2. Instantaneous power=im2 R sin2wt/2
3. Average power=0
4. The current is out of phase with the voltage.
6. current lag behind the voltage by 90°.
AC voltage applied to an capacitor:
i = im coswt
v = vmsinwt
1. im=vm/XC (XC=1/wC,the capacitive reactance)
2. Instantaneous power=im2 R sin2wt/2
3. Average power=0
4. The current is out of phase with the voltage.
6. current lead the voltage by 90°.
AC voltage applied to a LCR circuit:
q = qm cos(wt+o)
v = vm sinwt
im = vm/Z. [Z=[R2+(XL-XC)2](½)]
(Z=impedance)
vRm = imR ; vCm = imXC ; vLm = imXL
tan¢ = XC-XL
R
● If XC>XL; ¢is positive; circuit is purely capacitive
● If XC< XL;¢is negative circuit is purely inductive
Analytical method
● tan¢ = XC-XL
R
● 0 -¢ = π/2 ;¢ is phase constant
Resonance:
● Applied frequency becomes equal to the natural frequency of oscillation
● wL = 1/wC
● XL. = XC
● wo = 1/√LC,wo is resonant frequency
● Impedance is minimum; Z = R
● Bandwidth = 2∆w
● Quality factor Q= woL/R
Q = 1/woCR
Q = wo/2∆w
● greater the quality factor, greater will be the sharpness of the resonance
● Greater the inductance of the circuit greater the quality factor and hence the sharpness
of resonance
● Smaller the capacitance of the circuit greater the quality factor and hence sharpness of
resonance
● Smaller the bandwidth of the circuit, greater the quality factor and hence resonance
Power factor
● In LCR circuit the power is given by I2Zcos¢, here cos¢ is the power factor
● If ¢ = 0,cos¢=1, and the circuit is purely resistive ; power dissipation is maximum
● If ¢ = 90°,cos¢ = 0, the circuit will be purely capacitive or inductive; power dissipation is
minimum
● For LCR circuit power dissipation takes place through the resistor only
● For LCR circuit at resonance, the dissipation is maximum through resistor at resonance.
LC oscillations
● Possessed only by circuit having both inductor and capacitor.
● Inductor stores magnetic energy
● Capacitor stores electrical energy.
Oscillation in circuit
initially the capacitor is fully charged and when it is connected to the inductor the charge through
the capacitor decreases and the current begins to flow through the circuit at will induce a
magnetic flux in the inductor and the energy e gets stored as magnetic energy in inductor.This
process continues until the charge in the capacitor becomes zero and all the energy gets stored
as magnetic energy in inductor .once the inductor is fully charged the current through the circuit
will now be given to charge the capacitor and as a result the electrical energy will be stored in
the capacitor and the whole process continuous and this create an oscillation between the
charge and current in the circuit.
● Electrical energy is given by q2/2C
● Magnetic energy is given by (½)Li2.
Transformer
● device used to change alternating voltage from one value to another.
● Consists of primary and secondary coil
● Primary coil is input coil
● Secondary coil is output coil
● Np represents number of turns in primary coil and NS represents number of turns in
secondary coil.
Principle:
When an alternating voltage is applied to primary , the resulting current produces an
alternating magnetic flux in the secondary and it induces an emf.this EMF induces an EMF in
the primary called as back EMF.
Vs = NS = ip
Vp. Np. iS
● as the number of turns in the coil increases the voltage also increases and current
decreases
● In a step up transformer the number of turns in the secondary coil is more, so voltage
increases and the current decreases
● In a step down transformer, the number of turns in the secondary coil is less so voltage
decreases and the current increases.
In long distance transmission the signal is first stepped up(voltage increases and current
decreases) and on reaching and area substation near the consumer the voltage is stepped
down (voltage decreases and current increases) and is further stepped down at the receiver and
thus the power dissipation (i2R) will be less during the transmission.
