Resistance connected

in Parallel

 

1) Suppose R1, R2, & R3 resistors are connected parallelly, with a potential difference V of a battery. As shown in the diagram below

 





2) As same voltage is applied to all the resistors.



3) Therefore each resistors will have their own current amount say, I1, I2, & I3 passes through the resistors R1, R2, & R3 respectively.



4) Then sum of all these current will give the net current flowing through the circuit.

I  = I1  +  I2  +  I3



Now since potential is same for all these resistors so,

 






 

If   Rf   is the resultant resistance of these system, then


 


5) Now we get

I  = I1  +  I2  +  I3








6) Suppose there are n of resistors R1, R2, R3 ………… Rn  

connected parallelly then the resultant resultant resistance can be expressed as