Question

How to derive the formular I1=IR1/R1+R2

Answer 1

there are two resistances.  R1 and R2 connected in paralle.  There is a battery of potential  V  connected in parallel with both resistances.


current in the R1  : = i1 =  V/R1 
current in  R2:    I2 = V  / R2
So total current from battery  = I = V (1/R1 + 1/R2) = V (R1+R2)/R1R2
       So we get I1 = R2 I / (R1 + R2)

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If the two resistance are in series,  I1 = I2 = I.

Answer 2

Consider the current in R1 and R2 as I1 and I2.

Voltage across R1 is

V1=I1×R1

The equivalent resistance of circuit is

R=R1×R2/(R1+R2)

Total voltage of circuit is

V=I×R

But since the resistances are in parallel the voltage across R1 and R2 is same as supply voltage V.

Equating V and V1

I×R=I1×R1

I×R1×R2/(R1+R2)=I1×R1

Thus

I1=I×R2/(R1+R2)