special case of parallel circuit

Easy method to find resistance and branch current of parallel circuit:

parallel circuit

A frequent special case of parallel resistor is a circuit that contains in parallel.

Figure at the right side shows two resistor R1 and R2 are parallel across a battery of V volt .the total current I divided into two parts that is I1 flowing through R1 and I2 flowing through R2

for enlarge this picture click on the picture

1. Total resistance RT:

1/RT=1/R1+1/R2

        = (R2+R1)/ (R1*R2)

That means RT is

 RT= (R1*R2)/(R2+R1)

That means the total value of two resistors connected in parallel is equal to the product divided by the sum of two resistors.

2. Branch current:

RT= (R1*R2)/ (R1+R2)

   V=I*RT=I* (R1*R2)/R1+R2)

Current through R1, I1=V/R1

                                        =I*R1/ (R1+R2)                  [putting V=I*(R1*R2)/R1+R2]

Current through R2, I2=V/R2

                                      =I*R1/ (R1+R2)