ANALYSIS OF SERIES AND PARALLEL CIRCUITS

Analysis of series circuits:

       A series circuit is one which several resistance are connected one after to other .such connection is also end to end connection or cascade connection. There is only one path for flow of current.

Resistance in series:

       Considered the series resistance circuit given in below…

              

Characteristics of series circuit:

•            The same current flows through each resistance.
•     The supply voltage V is the sum of the individual voltage drops across the resistance.
•       V=V1+V2+V3+……+Vn
•             The Equivalent resistance equal to the sum of the individual resistance.
•              The equivalent resistance is the largest of all the individual resistance.
•        R>R1,R>R2,…….R>Rn

    

Inductor in series:

      Considered two inductors L1 and L2 are connected in series. The currents flowing through L1 and L2 are i1 and i2 while voltages developed across L1 and L2 are VL1 and VL2 respectively.

    The equivalent circuit is

     For series combination of  n inductance

            Leq=L1+L2+L3+……+Ln

Capacitance in series:

         Considered two capacitors C1 and C2 are connected in series. The current flowing through and voltages developed across C1and C2 are i1 and i2 and Vc1 and Vc2 respectively.

        The equivalent circuit is..

                    

                            Ceq=C1C2/C1+C2

Analysis of parallel circuits:

          The parallel circuit is one in which several resistance are connected across one another in such a way that one terminal of each is connected to form of junction point while the remaining ends are also joined to form of another junction point.

Resistors in parallel:

         In parallel connection of resistance R1,R2,R3…are connected in parallel combination is connected across a source of voltage source ‘V’.

In parallel circuit current passing through each resistance is different.let the total current is IT.These individual currents are I1,I2,I3,I4.While voltage across the two ends of each resistance R1,R2,R3,R4 is the same and equals the supply voltage.

Characteristics of parallel circuit:

1.     The same potential difference gets across all the resistance in parallel.
2.     The total current get divided into the no of paths equal to no of resistance in parallel circuit. The total current I is always sum of all the individual currents.
3.      I=I1+I2+I3…..+In
4.     The reciprocal of equivalent resistance of a parallel circuits is   equal to the sum of reciprocal of the individual resistance.
5.      The equivalent resistance is the smallest of all the resistance.
6.      R<R1,R<R2,R<R3…..R<Rn
7.   The equivalent conductance is the arithmetic addition of individual conductance.