Are uniform wire of resistance r is cut into two parts having length in ratio 2 is to 3 and connected in parallel combination the effective resistance of combination will be?

A wire that has resistance R is cut into two equal pieces. The two parts are joined in parallel. What is the resistance of the combination?

A wire that has a resistance, R is cut into two equal pieces.
The resistance of the each piece will be  `R/2` 

The two parts, each of resistance, R/2  are joined in parallel. 

The resistance of the parallel combination:  

`1/R^rho=1/R=1/R_1+1/R_2`

`Here R^1=R/2` 

   `=R_2=R/2` 

`1/Rrho=1/(R/2)+1/(R/2)` 

`1/Rrho=2/R+2/R` 

`1/Rrho=4//R`

`Rrho=R/4`  

Thus, the resistance of the combination will be R/4.

Concept: System of Resistors - Resistances in Parallel

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