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In a copper bar of square cross section,...

In a copper bar of square cross section, a smal cuboidal hole is drilled and is filled with aluminium (Al) as shown in the figure.
The electrical resistivities of Cu and Al are `1.7 xx 10^(-8) Omega` and `2.7 xx 10^(-8) Omega` m respectively. The electrical resistance between the two faces Pand Q of the composite bar is

A

2.34 `mu Omega`

B

13.5 `mu Omega`

C

8.5 `mu Omega`

D

5.21 `mu Omega`

Text Solution

Verified by Experts

The correct Answer is:
A
`R_(Cu)` and `R_(Al)` are parallel to each other.
`R=(R_(Cu)R_(Al))/(R_(Cu) + R_(Al)) = ((rhoCu^l)/(A_(Cu))xx rho_(Al^l)/(A_(Al)))/((rhoCu^(l))/(A_(Cu))+(rhoAl^l)/(A_(Al)))=(rhoCurhoAl^(l))/(rho_(Cu^A)Al + rhoAl^(A)Cu)`
`= (1.7 xx 10^(-8)xx 2.7 xx 10^(-8) xx 0.05)/({(1.7 xx 10^(-8)) xx (2^2 -1^2) + (2.7 xx 10^(-8))xx (1^2)}xx 10^(-4))`
`=2.42 xx 10^(-6) Omega = 2.42 muOmega`
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