Download AC Parallel Circuits

USE OF ICT IN EDUCATION FOR ONLINE AND BLENDED LEARNING-IIT BOMBAY
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
ASSIGNMENT( MODULE AC PARALLEL CIRCUIT )
Submitted by:
Dr. Deepak Kumar(Group Leader)
Dr. Vikash Kumar Gupta
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AC Parallel Circuits
• Impedances in parallel add together like resistors in
parallel.These impedances must be added vectorially.
• Whenever a capacitor and an inductor having equal
reactances are placed in parallel Equivalent circuit of the
two components is an open circuit.
• Conductance, G Reciprocal of the resistance
• Susceptance, B Reciprocal of the reactance
• Admittance, Y Reciprocal of the impedance
• Units for all of these are siemens (S)
AC Parallel Circuits
• In a Parallel circuit there are multiple pathways for charge to
flow
• Current goes through each of the branches at the same time
• Each device is placed on it’s own separate branch
Fig 4.1 Parallel Circuits
Parallel Circuit – Pros and Cons
Advantages
• The more devices (resistors) in a parallel circuit, does not
decrease the current (does not dim bulbs).
• If one resistor breaks (a bulb goes out) the rest do not.
Problems
• Current doesn’t stay the same for entire circuit
– So energy is used up quicker
– So the total current increases = faster electrons = hotter
wire = fire?
Parallel Circuit - Resistance
• Resistors added side-by-side
• The more paths, the less TOTAL resistance.
1/ Req=1/R1+1/R2+1/R3
• Since the circuit offers two equal pathways for charge flow, only 1/2
the charge will choose to pass through a given branch
Fig 4.2 Two resistors connected in parallel
Parallel Circuit - Current
• ALL paths are used!
– But the charge divides up into all branches
– One branch can have more current than another
branch (depends on resistance in branch).
• Total current = sum of current in each path
IT = I 1 + I2 + …
Fig.4.3 Various loads connected in parallel
Parallel Circuit - Voltage
• A charge only passes through a single resistor.
• Voltage drop across the resistor that it chooses to
pass through must equal the voltage of the battery.
• Total voltage = the voltage across each individual
resistor
VT = V1 = V2 = …
Fig 4.4 Same voltage potential connected across resistors connected in parallel
Example
Find the combined impedance of the following circuit:
Parallel Resonance
Parallel Resonance
1
LC
w 
O
Q
Series Resonance
O
wL
R
Q  w RC
O
o
R
BW  ( w  w )  w 
L
2
1
LC
w 
1
1
BW  w 
RC
ww
,w
1
2
BW
BW
 R  R 
1 
w ,w  
   

2
L
2
L
LC




 1
1 
 1 
w ,w  
 
 

 2 RC  LC 
 2 RC
1

 1 
w ,w  w   
 1
 2Q 
 2Q

1

 1 
w ,w  w   
 1
 2Q 
 2Q

2
1
2
2
1
2
o
2
1
2
2
1
2
o
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PARALLEL RESONANCE
Consider the circuits shown below:
Fig 4.5 Current and voltage relationship of circuit connected in
parallel
V
I
R
L
1
1 
I  V   jwC 

R
jwL


C
L
R
V
C
I

1 
V  I  R  jwL 

jwC


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Parallel RLC Circuit
•Like the series RLC circuit, we can solve this circuit using the
phasor or vector method but this time the vector diagram will
have the voltage as its reference with the three current vectors
plotted with respect to the voltage.
•The phasor diagram for a parallel RLC circuit is produced by
combining together the three individual phasors for each
component and adding the currents vectorially.
Fig 4.6 Parallel RLC circuit
Phasor Diagram for a Parallel RLC
Circuit
Fig 4.7 Phasor Diagram of parallel RLC circuit
Impedance of a Parallel
RLC Circuit
Admittance of a Parallel RLC
Circuit
Admittance Triangle for a Parallel RLC
Circuit
Fig 4.8 Admittance and Impedace triangle of parallel RLC circuit
Giving us a power factor
angle of:
Example:
A 50Ω resistor, a 20mH coil and a 5uF capacitor
are all connected in parallel across a 50V, 100Hz
supply. Calculate the total current drawn from
the supply, the current for each branch, the total
impedance of the circuit and the phase angle.
Also construct the current and admittance
triangles representing the circuit
1). Inductive Reactance, ( XL ):
2). Capacitive Reactance, ( XC ):
4). Current through resistance, R ( IR ):
5). Current through inductor, L ( IL ):
6). Total supply current, ( IS ):
(7)Conductance, ( G ):
(8). Admittance, ( Y ):
9). Phase Angle, ( φ ) between the resultant current and the supply voltage:
Current and Admittance Triangles
Fig 4.9 Current and Admitance triangle of the given circuit
Thank You
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