Conducting wire of uniform cross sectional area $2 c m^{2}$ and length $1 c m$ carries a current of $8 A$ and has a potential difference of $2 V$ . The resistivity of the material of the wire is:

0.5 Ω c m

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0.05 Ω c m

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0.5 Ω m

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0.05 Ω m

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Solution

The correct option is A $0.5 Ω c m$
Given:
Cross-sectional area of the wire $S = 2 c m^{2}$
Length of the wire $l = 1 c m$
Current in the wire $I = 8 A$
Voltage $V = 2 v o l t$

Resistance is given by:
$R = ρ \frac{l}{S}$
Also, according to Ohm's law:
$R = \frac{V}{I}$

$∴ \frac{V}{I} = ρ \frac{l}{S}$
$ρ = \frac{V S}{I l}$
$ρ = \frac{2 \times 2}{8 \times 1}$
$ρ = 0.5 Ω c m$

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Conducting wire of uniform cross sectional area 2 cm2 and length 1 cm carries a current of 8 A and has a potential difference of 2 V. The resistivity of the material of the wire is:

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