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Q.

There are three cylinders which have different shapes namely ( $a$ ), ( $b$ ) and ( $c$ ), which cylinder has the highest resistance?

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a

a

b

b

c

c

d

None of the above

answer is B.

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Detailed Solution

Of all the given three cylinders having different shapes namely (

a

), (

b

) and (

c

), cylinder (

b

) will have the highest resistance.
It is well known that “the resistance of the material is directly proportional to the resistivity of the material, length of the conductor and inversely proportional to the cross-sectional area.”
The resistance for the figure (

a

) is

R_{a} = \frac{ρL}{A}

The resistance for the figure (

b

) is

R_{b} = ρ (\frac{3 L}{\frac{A}{3}})

{\Rightarrow R}_{b} = \frac{9 ρL}{A}

The resistance for the figure (

c

) is,

R_{c} = ρ (\frac{L / 3}{3 A})

\Rightarrow R_{c} = \frac{ρL}{9 A}

Therefore, the increasing order of the resistance for the three cylinders is,

R_{b} > R_{a} > R_{c}

Hence, the cylinder (

b

) will have the highest resistance among the given cylinders.

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