Question

how to prove the formula of resistors in parallel

Answer 1

if resistors are in parallel then 1/R = 1/R1 +1/R2 + 1/R3 . 
 
to prove this, we know that if resistors are connected in parallel , the voltage remains constant but current through each resistance varies 
so therefore,
                            I = I1 + I2+ I3
                         
                         v/r = v/r1 + v/r2 + v/r3
                        v/r  = v ( 1/r1 + 1/r2 + 1/r3 )
             therefore,
                     1/r = 1/r1 + 1/r2 + 1/r3.



hope it is useful!