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

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 = I1 + 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 Series Resonance

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

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

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

Admittance of a 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