1. 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

2. 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)

3. 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

4. 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?

5. 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

6. 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 = I1 + I2 + …
Fig.4.3 Various loads connected in parallel

7. 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

8. Example
Find the combined impedance of the following circuit:

9. Parallel Resonance
Parallel Resonance
Series Resonance

10. PARALLEL RESONANCE Consider the circuits shown below:
Fig 4.5 Current and voltage relationship of circuit connected in parallel V I R L C L R V C I

11. Fig 4.6 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

12. Phasor Diagram for a Parallel RLC Circuit
Fig 4.7 Phasor Diagram of parallel RLC circuit

13. Admittance of a Parallel RLC Circuit
Impedance of a Parallel RLC Circuit
Admittance of a Parallel RLC Circuit

14. Admittance Triangle for a Parallel RLC Circuit
Fig 4.8 Admittance and Impedace triangle of parallel RLC circuit

15. Giving us a power factor angle of:

16. 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 ):

17. 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:

18. Current and Admittance Triangles
Fig 4.9 Current and Admitance triangle of the given circuit

19. Thank You