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USE OF ICT IN EDUCATION FOR ONLINE AND BLENDED LEARNING-IIT
BOMBAY
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
ASSIGNMENT( MODULE AC SERIES CIRCUIT)
Submitted by:
Dr. Deepak Kumar(Group Leader)
Dr. Vikash Kumar Gupta
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AC Circuits
• Rules and laws developed for dc circuits apply equally well for ac
circuits.
• Analysis of ac circuits requires vector algebra and use of complex
numbers.
•Voltages and currents in phasor form.
•Expressed as RMS (or effective) values.
Fig 3.1 Example of AC circuit
Phasor Diagram of Resistor
• Voltage and current of a resistor will be in phase
• Impedance of a resistor is: ZR = R0°
I 
V
 I
R0
Figure 3.2 Phasor diagram of resistance
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Phasor Diagram of Inductor
• Current through an inductor lags the voltage by 90°
XL  j  L
Z L  X L 90
I
V
X L 90
I  I  90
Fig 3.3 Phasor Diagram of Inductor
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Phasor Diagram of Capcitor
•
Current through a capacitor leads the voltage by 90°
1
XC 
jC
Z C  X C   90
V
I
X C   90
I  I  90
Fig 3.4 Phasor Diagram of Capacitor
Frequency Effects on Capacitive
Reactance
• Impedance of a capacitor decreases as the frequency increases.
• For dc (f = 0 Hz), impedance of the capacitor is infinite
Fig 3.5 Variation of capacitive reactance with frequency
• For a series RC circuit, total impedance approaches R as the
frequency increases
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Frequency Effects on Inductive
Reactance
• Impedance of an inductor increases as frequency increases.
• At dc (f = 0 Hz), inductor looks like a short. At high
frequencies, it looks like an open.
Fig 3.6 Variation of inductive reactance with the variation of frequency
AC Series Circuit
• Impedance vectors will appear in either the first or the fourth
quadrants because the resistance vector is always positive.
• When impedance vector appears in first quadrant, the circuit is
inductive.
• If impedance vector appears in fourth quadrant, the circuit is
capacitive
AC Series Circuit
• Current everywhere in a series circuit is the same.
• Impedance used to collectively determine how resistance,
capacitance, and inductance impede current in a circuit.
Z  R  jX
X  XL  XC
XL  j  L
XC 
1
jC
Where L and C are inductance and capacitance of the circuit elements
AC Series Circuit
• Total impedance in a circuit is found by adding
all individual impedances vectorially.
•
Zeq  Z1  Z 2  Z 3  ........Zn
Voltage Divider Rule
• Voltage divider rule works the same as with dc circuits.
• From Ohm’s law:
I x  IT
Vx
VT

Zx
ZT
Vx
Zx

VT
ZT
Kirchhoff’s Law
• KVL is same as in dc circuits.
• Kirchoff’s Voltage Law: Phasor sum of voltage drops and
rises around a closed loop is equal to zero.
• Voltages may be added in phasor form or in rectangular form.
 VA  VB  VC  0
Fig 3.7 Kirchhoff’s Voltage law in AC circuit
Kirchhoff’s Law
• KCL is same as in dc circuits.
• Kirchhoff’s Current Law : Summation of current phasors
entering and leaving a node is equal to zero.
• Currents must be added vectorially-currents entering are
positive, and currents leaving are negative
Fig 3.8 Kirchhoff’s Current Law in Ac Ccircuit
Remarks
• In a series RL circuit, impedance increases from R to a larger
value
• In a parallel RL circuit, impedance increases from a small
value to R
Corner Frequency
• Corner frequency is a break point on the frequency response
graph.
• For a capacitive circuit
C = 1/RC = 1/
• For an inductive circuit
C = R/L = 1/
Series Resonance
• In a circuit with R, L, and C components combined in seriesparallel combinations, impedance may rise or fall across a
range of frequencies.
• In a series branch
– Impedance of inductor may equal the capacitor.
– Impedances would cancel leaving impedance of resistor as
the only impedance.
– Such condition is referred to as resonance
Series resonance
Fig 3.9 Resonating frequency in AC series circuit.
• Expression for Resonating Frequency
Thank You
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