In an aluminium (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure. The electrical resistivities of Al and Fe are `2.7 xx (10^-8) Omega m and 1.0 xx (10^-7) Omegam,` respectively. The electrical resistance between the two faces P and Q of the composite bar is

Options

A. `2475/64 mu Omega`
B. `1875/64 muOmega`
C. `1875/49 muOmega`
D. `2475/132 muOmega`

Answer

B

Explanation

(b) `R_(Fe) = (rho_(Fe) xx l_(Fe))/A_(Fe) = (10^(-7) xx 50 xx 10^(-3))/( 4 xx 10^(-6)) = 25/2 xx 10^(-4)`
`R_(Al) = (rho_(Al) xx l_(Al))/(A_(Al)) = (2.7 xx 10^(-8) xx 50 xx 10^(-3)) /((49-4) xx 10^(-6)) = (2.7 xx 50)/(45) xx (10^(-5))`
`= 0.3 xx 10^(-4)`
`R_(t otal) = (R_(Fe) xx R_(Al))/(R_(Fe) + R_(Al)) = (12.5 xx 10^(-4) xx 0.3 xx 10^(-4))/(12.8 xx 10^(-4)) ~~ 29 muOmega`.