Two wires of same length and thickness having specific resistances and respectively are connected in parallel. The effective resistivity is . The value of , to the nearest integer, is ________.
Step 1: Given
Specific resistance of a first wire:
Specific resistance of a second wire:
Effective resistivity:
Resistance of first wire is .
Resistance of second wire is .
Step 2: Formula Used
The resistance of a wire is given by , where is resistivity, is length of wire and is area of cross-section.
Equivalent resistance when connected in parallel:
Step 3: Find the effective resistivity
Find an expression for the effective resistivity using the formula . The area of the system will be twice the area of wires as 2 wires are connected together, so the area for effective resistance will be but the length will remain the same as they are connected in parallel.
Substitute for , for and for .
Calculate the effective resistivity by substituting the values in the obtained expression
Hence, the value of is .