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Series-Parallel Circuits

In practice we come across combined circuits, known as series- parallel circuits, which are very complicated in solution. The circuit of this type is shown in. To solve such circuits, the following method illustrating the solution of method illustrating the solution of circuit shown in must be adopted.

Series-Parallel Circuit

First of all equivalent resistances of all parallel branches are determined separately e.g., of branches AB and CD by the laws of parallel circuits discussed in Art.

Equivalent resistances of parallel branch AB,

RAB =   1     =   R1R2
          1 + 1     R1+R2

and equivalent resistance of parallel branch CD

RCD =    1  =    R4 R5 R6
         1+1+1  R5R6+ R4R6+R4R5  
        R4 R5 R6

Now the circuit shown in gets reduced to a simple series circuit shown in consisting of three resistance,

RAB  =   R1 R2  , Rac = R2 and RCD   R1 R2 R3
            R1+R                                   R5R6+ R4R6+R4R5

Total resistance of the circuit, RT = RAB + RBC + RCD

Now circuit current may be determined from the relation, I = V
After knowing I, potential differences across branches AB, BC and CD are determined form the relations.

P.D. across AB. VAB = I. RAB = V . RAB

P.D. across CD, Vac = I. Rac = V .Rac

and P.D. across CD, VCD = I. RCD = V . RCD

After determination of potential difference across each parallel branch, the currents the various resistances are determined from the relations,

Current in resistance    R1 = I1 =VAB

Current in resistance     R2 = I2 VAB

Current in resistance      R3 = I3 = I

Current in resistance     R4 = I =VCD

Current in resistance      R5 = I5 = VCD

and current in resistance  R6 = I6 = VCD

Thus equivalent resistance of the whole circuit, voltage drop across each branch and currents in the various resistors may be determined.

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