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Resistance

A conductor w...

Question

A conductor with rectangular cross-section has dimensions $(a \times 2 a \times 4 a)$ as shown in figure. Resistance across AB is $R_{1}$ , across CD is $R_{2}$ and across EF is $R_{3}$ . Then which of the following is true?

R_{1} = R_{2} = R_{3}

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R_{1}

R_{2}

R_{3}

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R_{2}

R_{3}

R_{1}

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R_{1}

R_{3}

R_{2}

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Solution

The correct option is B $R_{1}$ > $R_{2}$ > $R_{3}$

Resistance $R = ρ \frac{l}{A}$
From the figure the dimensions are $a$ , $2 a$ and $4 a$ , i.e.
Distance between faces A and B = $4 a$
Distance between faces C and D= $2 a$
Distance between faces E and F= $a$

As $R \propto l$ , AB having the highest length will have the most resistance followed by CD and EF being of the lowest length will have the least resistance. So, the order is $R_{1} > R_{2} > R_{3}$ .

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