CBSE Class 10 Answered

Derivation of the Parallel Resistance Formula

It’s easy to see where the series resistanceformula comes from; add a resistor, add its resistance.  It’s more difficult to see where the parallel resistance formula comes from.  However, the formula can be derived using a simple combination of KCL and Ohm’s law.  Take the simple circuit shown in Figure 11.   KCL says that the total current in the circuit must be equal to the currents I₁ and I₂.

From KCL:           

Using Ohm’s law gives equations for I_s, I₁, and I₂.

From Ohm’s Law:      

Plug these three equations back into the first equation and solve for R₁||R₂ to derive the formula for two parallel resistors.

 Which gives us…

If two resistors in series then current is same in both resistors.
V1=I*R1
V2=I*R2

V=V1+V2
I*R=I*R1+I*R2
R=R1+R2