Pursue of Basic Law: Series and Parallel with Example

  Basic Law: Series and Parallel

In series resistor same current but not in voltage.



V1=iR1 & V2=iR2
Using KVL
     V-V1-V2=0
     V=i(R1+R2)
     V/(R1+R2)=v/Req
     or V=i(R1+R2)=iReq
     Req=R1+R2
    Because the voltage is not equal so we use the voltage division:
        V1=iR1   and V2=iR2
         i=V/(R1+R2 )

     V1=VR1/(R1+R2)
     V2=VR2/(R1+R2)
In parallel resistor same voltage but not in current

















V=i1R1=i2R2
     i2+i2
     V/R1+R2
     V/R1+V/R2
    R(I/R1+ I/R2)
    V/Req
     V=iReq
    I/Req=I/R1+1/R2
    Req=R1R2/(R1+R2)

     The current is not the same so to solve the current we use the current division:
      V=i1R1=i2R2
      V=iReq=iR1R2/(R1+R2)
      and i1=V/R1  and   i2=V/R2

          i1=iR2/(R1+R2)
          i2=iR1/(R1+R2)

Conductance(G)

Series Coductance 
         1/Geq = G1+G2+...Gn
Parallel Conductance
          Geq =G1+G2+....Gn




Example 1:







Use KVL
    -15+(1+5+2)I+Vx=0
      Vx=51
             -15+81+101=0,     I= 5/6
              Vx=51=25/6=4.17V