Two conducting wires A and B (made of same mate-rial ) of lengths 1 m and 2 m and area of cross sec-tions `1 cm^(2)` and `100 mm^(2)`, respectively are taken. If the resistance of a wire of length 5 m and thickness 2 cm made of same material as A and B is `50 ohm`, then find the resistance of the new wire of length 5 m formed by melting A and B.

Explanation

(i) Volume of new wire `(C ) = V_(C ) = V_(A) + V_(B)`
(ii) area of cross section of new circle ( C )
`= A_(C) = (V_(A) + V_(B))/(l_(C))`
(iii) `R = rho'l/A`
(iv) Find the value of `rho` from given information
`rho = (RA)/(l)`
`= (50 Omega xx 22/7 xx 1 cm^(2))/(500 m)`
(v) we know, `R_(C ) = rho'(l_(C))/(A_(C))`
substitute the values and find the value of `R_(C)`.
(vi) `25 Omega`.