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Question

A Conductor with rectangular cross-section has dimensions (a×2a×4a) as shown in figure. Resistance across AB is x, across CD is y and across EF is z. Then


A
x=y=z
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B
x>y>z
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C
y>z>x
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D
x>z>y
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Solution

The correct option is D x>z>y
Formula of resistance is

R=Resistivity×lengthArea of cross-section=ρlA

Length l is along the direction of flow of current.
Area A is perpendicular to direction of flow of current.

For resistance across AB:

A=2a2; l=4a

RAB=ρ×4a2a2=2ρa=x

Similarly,

RCD=ρ×a8a2=ρ8a=y

REF=ρ×2a4a2=ρ2a=z

From above expression, we get

x>z>y

Hence, option (d) is correct.

Why this Question ?Same piece of a conductor can have differentresistances depending on the points between which we have to find.

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