AC Circuit
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Alternating Current & Alternating Voltage
Definition : An Alternating Current in any circuit is current which varies both in magnitude and polarity with respect to time. Similarly, alternating voltage is voltage that varies both in magnitude and polarity with respect to time. The reversal of polarity of voltage or current occurs at regular intervals of time. The circuit in which AC flows is called Alternating Circuit.
Equations : Consider a rectangular coil, having N turns and rotating in a uniform magnetic field, with an angular velocity of . Let be maximum flux linked with the coil and be flux linked with the coil at any time , then According to Faraday's Law of Electromagnetic Induction, e.m.f. induced in the coil is given by rate of change of flux For maximum e.m.f., Similarly, -
RMS Values & Average Values
Average Values
Instant Value =
For whole cycle the average value will be as the area under the first cycle is . So, taking first half of the cycle from (as average = sum of instant values / no. of instant values)
Root Mean Square Values :
Squaring both the sides Taking average of given value : On taking square root -
Form Factor & Peak Factor
Form Factor : Ratio of RMS value to the average value of altenating quantity
Peak Factor : Ratio of Peak or Maximum value to RMS value of an alternating quantity -
Active & Reactive components of Circuit Current
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Power Factor & Quality Factor
Power Factor : a) Cosine of the phase angle between
and i.e. b) Ratio of Resistance to Impedance c) Ratio of active power to apparent power Note : P.F. cannot be greater than 1
Quality Factor : Reciprocal of Power factor is Quality Factor Also, -
Active, Reactive & Apparent Power
Apparent Power : the product of RMS values of applied voltage and circuit current
Active Power : the product of apparent power and the power factor
it is due to the resistive part of the circuit Reactive Power : the product of apparent power and the sin of phase difference between and
also called as "Wattless Power" -
AC Circuit containing purely Resistive load
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AC Circuit containing purely Inductive load
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AC Circuit containing purely Capacitive load
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R-L Circuit
Consider a circuit consisting of resitor
and an inductive coil of inductance connected in series. Since it includes inductor will lag behind by some phase difference Power Factor :
Sample Problem :
A
resitor is connected to inductor across voltage source in series. Find
(a) Input current
(b) Voltage drop across inductor and resistor
(c) Power Factor
(d) Power consumedSolution :
(a) Input Current : (b) Voltage Drop across Resistor Voltage Drop across Inductor : (c) Power Factor (d) Power consumed = -
R-C Circuit
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R-L-C Circuit
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Three Phase AC Circuit
We study two types of connections in 3 phase systems: Star and Delta connection.
Star Connection
All the three terminals are connected to a common point. Also called as Y connection.
Line Currents :
Line Voltages :
Phase Currents :
Phase Voltages :
Relationship between Line and Phasor Currents
As we can see from the diagram
Relationship between Line and Phasor Voltages
As Power : Active Power in 1 phase =
Active Power in 3 phase, Reactive Power : Apparent Power :
Delta Connection
Line Currents :
Line Voltages :
Phase Currents :
Phase Voltages :
Relationship between Line and Phasor Voltages
As we can see from the diagram
Relationship between Line and Phasor Currents
As Power : Active Power in 1 phase =
Active Power in 3 phase, Reactive Power : Apparent Power :