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A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts. Which of the following quantities remain constant in the wire? (a) drift speed (b) current density (c) electric current (d) electric field - Physics

A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts.
Which of the following quantities remain constant in the wire?
(a) drift speed
(b) current density
(c) electric current
(d) electric field
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Solution

The electric current will remain constant in a wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts.

Because current is the only quantity that does not depend on the area of cross- sections of the wire.
`I=(dq)/(dt)`, that is the rate of flow of charge, where as drift speed, current density and electric field are depends on the increasing area of cross-section with the following relations:

Drift speed : `ν_d=I/(An""e)`
Current density = `I/A`
Electric field = `J/σ`

Concept: Drift of Electrons and the Origin of Resistivity
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