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Current is fl...

Question

Current is flowing through a conductor of non-uniform cross-section. If $A_{1} > A_{2}$ , then the relation between the drift velocity $(V)$ and current at the two cross- sections respectively, will be

V_{1} > V_{2}

and

i_{1} > i_{2}

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V_{1} < V_{2}

and

i_{1} = i_{2}

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V_{1} < V_{2}

and

i_{1} < i_{2}

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V_{1} = V_{2}

and

i_{1} = i_{2}

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Solution

The correct option is B $V_{1} < V_{2}$ and $i_{1} = i_{2}$

Given: $A_{1} > A_{2}$

According to the conservation of charge principle, charge crossing through any cross-section per unit time will be equal.

$\Rightarrow i_{1} = i_{2} = i$

Now current density, $J = \frac{i}{A}$

Thus, $J_{1} = \frac{i}{A_{1}}$ & $J_{2} = \frac{i}{A_{2}}$

$(∵ A_{1} > A_{2})$

$∴ J_{1} < J_{2}$

From the relation of drift speed,
$V_{d} = \frac{J}{n e}$

$\Rightarrow V_{d} \propto J$

Hence, $V_{1} < V_{2}$

Hence, $(B)$ is the correct answer.

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