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  4. A conducting wire of length T, area of crosssection A and electric resistivity ρ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be:

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Q. A conducting wire of length $T$, area of crosssection $A$ and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference $V$ is developed between its ends, causing an electric current.
If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be:

JEE MainJEE Main 2021Current Electricity

Solution:

As per the question
image
Resistance $=\frac{\rho(2 l)}{( A / 2)}=\frac{4 \rho l}{ A }$
$\Rightarrow $ Current $=\frac{ V }{ R }=\frac{ VA }{4 \rho l}$