Parallel Circuit

A Parallel circuit is a circuit in which there are at least two independent paths in the circuit to get back to the source. in a parallel circuit, the current will flow through the closed paths and not through the open paths.

 


The following rules apply to a parallel circuit:
1) The potential drops of each branch equals the potential rise of the source





2)The total current is equal to the sum of the currents in the branches.

3) The inverses of the total resistance of the circuit (also call effective resistance) is equal to the sum of the inverses of the individual resistances.




Example: Calculate the total resistance of the circuit when R1,R2,R3 are 100 (ohm) and Voltage 1000 v. calculate the total current and each branch  of current and each branch voltage drop and total power of the following figure .

Solution: 

            1/Rt = (1/R1 + 1/R2 + 1/R3) ohm
                    = (1/1oo + 1/100 +1/100) ohm
                    = ( 3/100) ohm
               Rt  = (100/3) ohm
                    = 33.334 ohm

in this circuit total Resistance is 33.334 ohm.

 so total current in this circuit are:
 It = V/Rt
    = 1000 / 33.334
   = 29.99 Amp
or 30.00 amp
in this circuit three resistance value is same so current is equal to each branch
                              3o/3 = 10
   I1= 10 amp.  I2= 10 amp. I3 = 10 amp.

Voltage drop for R1:
 Vr1 = I1* R1 =10*100=1000 Volt
Voltage drop for R2:
 Vr2 =I2* R2 =10*100=1000 Volt
Voltage drop for R3:

 Vr3 =I3* R3 =10*100=1000 Volt
 
Total Power of this circuit is
 P= VI
   = 1000*30
   =30000
   =30.000 KW