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Network Simplification

Network reduction or simplification is a process by which currents and voltage acting in a circuit composed of resistors having a series, parallel of series-parallel connections can be determined.

It may be seen form that resistances R4 and R5 are connected in series and the same current (Ia) flows through them because the circuit does not branch off at points C and D. By virtue of this fact, the three resistances R3, R4 and R5 can be combined into a single equivalent resistance given by the expression

R = R2+R4+R5

Thus a simpler equivalent circuit shown in is obtained. Form circuit diagram shown in it can be seen that resistance R2 is connected in parallel with the series combination of resistances R3, R4 and R5 i.e. equivalent resistance R. Resistances R2 and R1 can be combined into a single equivalent resistance given by the expression

R = R2R’ R2(R3+R5)
     R2+R1‘  R2(R3+R5)

Thus the circuit is further simplified. Resistances R1, R" and R6 in the circuit of are seen to be connected in series. Replacing all the three resistances by a single equivalent resistance connected a cross the battery (supply source), a simple series circuit is obtained where in

R " = R1+R6+R"

In a similar way most of the series-parallel circuits containing a single supply source can be reduced to a simple series circuit.

Now the current in the simple series circuit, shown in, can be readily determined by a plying Ohm’s law, Now the branch currents can be determined by restoring the circuit step by step to its original form in the reverse order.

It is evident form circuit diagram shown in


Further more, the voltage across points B and E will be I, R” knowing the voltage across points B and E, currents I2 and I3 can be easily determined from the expressions

I2 = I1R" and I3 = I1R"  =      I1R"      
        R               R"      R3+R4+R5

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