1.

Specific resistance of material of one wire is rho. Its volume is 3 m^(3) and its resistance is 3 Omega. Its length would be ..... .

Answer»

`SQRT((1)/(rho)) `
`(3)/(sqrt(rho))`
`(sqrt(3))/(rho)`
`(rho)/(sqrt(3))`

Solution :`(3)/(sqrt(rho))`
volume V = AREA A `xx ` LENGTH L
`therefore A= (V)/(l)= (3)/(l) ""` ... (1)
`rArr R = (rho l)/(A) = (rho l)/((3)/(l))"" [ because " from equation (1)" ] `
`therefore 3 = (rho l^(2))/(3) "" [ because R= 3 Omega ] `
`therefore l^(2)= (9)/(rho)`
`therefore l = (3)/(sqrt(rho))`


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