A nichrome wire 50 cm long and one square millimetre cross- section carries a current of 4 A when connected to a 2 V battery. The resistivity of nichrome wire in ohm metre is

Options

A. `1xx10^(-6)Omegam`
B. `2xx10^(-7)Omegam`
C. `4xx10^(-7)Omegam`
D. `5xx10^(-7)Omegam`

Answer

A

Explanation

Here, `l=50cm=50xx10^(-2)m`
`A=1mm^(2)=1xx10^(-6)m^(2),V=2V,I=4A`
According to Ohm.s law, `V=IR`
or `R=(V)/(I)=(2)/(4)=(1)/(2)Omega" "...(i)`
Resistance of a wire is `R=rho(l)/(A)orrho(l)/(A)=(1)/(2)` (Using (i))
`therefore rho=(A)/(2l)=(10^(-6))/(2xx50xx10^(-2))=10^(-6)Omegam`