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

(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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