The potential difference across a wire of $10^{- 3} c m^{2}$ cross-sectional area and 50 cm length is 2 V, when a current of 0.25 A exists in the wire.The conductivity of the material in $Ω^{- 1} m^{- 1}$ is

2.5 \times 10^{6}

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6.25 \times 10^{5}

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2.5 \times 10^{9}

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6.25 \times 10^{10}

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Solution

The correct option is B $6.25 \times 10^{5}$
We know,
$R e s i s t a n c e (Ω) = \frac{l}{σ a} = \frac{P o t e n t i a l D i f f e r e n c e (V)}{C u r r e n t (A)}$
Where, l = lenghth in meter = 0.5 m
$σ$ = conductivity in $Ω^{- 1} m^{- 1}$
a= area in $m^{2} = 10^{- 7}$
$\Rightarrow σ = \frac{l A}{V a} = \frac{0.5 \times 0.25}{2 \times 10^{- 7}}$

$\Rightarrow σ = 6.25 \times 10^{5} Ω^{- 1} m^{- 1}$
Therefore, B is correct option.

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The potential difference across a wire of 10−3cm2 cross-sectional area and 50 cm length is 2 V, when a current of 0.25 A exists in the wire.The conductivity of the material in Ω−1m−1 is

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