With the help of a circuit dillgram prove that when a number of resistors are connected in parallel, the reciprocal of equivalent resistance of the combination is equal to the sum of the reciprocals of the individual resistances of the resistors. Find the resistance between A and B in the following network.

Explanation

If there are two resistances in parallel i.e. `R_(1)` and `R_(2)`
`:. ` Equivalent resistance R :

`(1)/(R) = (1)/(R_(1))+(1)/(R_(2))`
Where `R_(1)=2Omega+2 Omega= 4 Omega`
`(1)/(R) =(R_(2)+R_(1))/(R_(1)+R_(2))`
Now `R = (R_(1)R_(2))/(R_(1)+R_(2))`
Resistance across A and B :
`R = (4xx4)/(4+4)= (16)/(8) = 2 Omega`