CBSE Class 12 · 2017 · Current ElectricityShort Answer

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Derive the expression for the current density of a conductor in terms of the conductivity and the applied electric field. Explain, with reason, how the mobility of electrons changes when the potential difference applied is doubled at constant temperature.

Answer: $J = σ E$ . Mobility does not change — it depends only on $τ$ (and hence temperature), not on the applied voltage.

Solution

From

V = I R = \frac{I ρ ℓ}{A}

and

V = E ℓ

, we get

E ℓ = \frac{I ρ ℓ}{A}

, i.e.

E = \frac{J ρ}{1} = \frac{J}{σ} \Rightarrow J = σ E

. Mobility

μ = \frac{v _{d}}{E} = \frac{e τ}{m}

depends only on

τ

, which is fixed by the temperature. Doubling

V

doubles both

E

and

v_{d}

, so their ratio

μ

is unchanged.

CBSE Class 12 Board · 2017 · Subjective

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