## Network Simplification

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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 R

R = R

Thus a simpler equivalent circuit shown in is obtained. Form circuit diagram shown in it can be seen that resistance R

R =

R

Thus the circuit is further simplified. Resistances R

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

I

Further more, the voltage across points B and E will be I, R” knowing the voltage across points B and E, currents I

I

R

For more help in

It may be seen form that resistances R

_{4}and R_{5}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 R_{3}, R_{4}and R_{5 }can be combined into a single equivalent resistance given by the expressionR = R

_{2}+R_{4}+R_{5}Thus a simpler equivalent circuit shown in is obtained. Form circuit diagram shown in it can be seen that resistance R

_{2}is connected in parallel with the series combination of resistances R_{3}, R_{4}and R_{5}i.e. equivalent resistance R. Resistances R_{2}and R_{1}can be combined into a single equivalent resistance given by the expressionR =

__R__=_{2}R’__R___{2}(R_{3}+R_{5})R

_{2}+R_{1}‘__R___{2}(R_{3}+R_{5})Thus the circuit is further simplified. Resistances R

_{1}, R" and R_{6}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 inR

^{"}= R_{1}+R_{6}+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

I

_{1}+I_{2}+I_{3}Further more, the voltage across points B and E will be I, R” knowing the voltage across points B and E, currents I

_{2}and I_{3 }can be easily determined from the expressionsI

_{2}=__I__and I_{1}R"_{3}=__I__=_{1}R"__I___{1}R"R

_{3 }R" R_{3}+R_{4}+R_{5}For more help in

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