Consider a thin square sheet of side L and thickness $t$ , made of a material of resistivity $ρ$ . The resistance between two opposite faces, shown by the shaded areas in the figure, is [2010]

Question

Smart Achievers · Accepted Answer

(3)

We know that resistance, $R = ρ \frac{l}{a}$

Here, $l = L$ and $a = L \times t$

Therefore, $R = \frac{ρ L}{L \times t} = \frac{ρ}{t}$

Hence, R is independent of L and inversely proportional to $t .$

Solution

Q.
Consider a thin square sheet of side L and thickness $t$ , made of a material of resistivity $ρ$ . The resistance between two opposite faces, shown by the shaded areas in the figure, is [2010]

1 directly proportional to $L$

2 directly proportional to $t$

3 independent of $L$

4 independent of $t$

Ans.
(3)

We know that resistance, $R = ρ \frac{l}{a}$

Here, $l = L$ and $a = L \times t$

Therefore, $R = \frac{ρ L}{L \times t} = \frac{ρ}{t}$

Hence, R is independent of L and inversely proportional to $t .$

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Solution

Q. Consider a thin square sheet of side L and thickness t, made of a material of resistivity ρ. The resistance between two opposite faces, shown by the shaded areas in the figure, is [2010]

1 directly proportional to L

2 directly proportional to t

3 independent of L

4 independent of t

Ans. (3) We know that resistance, R=ρla Here, l=L and a=L×t Therefore, R=ρLL×t=ρt Hence, R is independent of L and inversely proportional to t.