Question

drive an expression for combination of resistor in parallel

Answer 1

let's resistances are r1,r2,r3 connected in parallel.
I = v / r
I1 = v/ r1
I2 = v / r2
I3 = v / r3
I1+I2+I3 = v / r+v/ r1+v / r3.
I = v(1/r1+1/r2+1/r3) (I = I1+I2+I3)
v/r = v(1/r1+1/r2+1/r3) (I = v / r)
1/r = (1/r1+1/r2+1/r3) ( v is constant in parallel combination)
so resultant resistance is 1/r = (1/r1+1/r2+1/r3)