Drift velocity is ~10⁻⁴ m/s yet the bulb lights instantly? Also what happens to v_d if wire length doubles?

8 answers & replies

• [+][–]Nisha Verma12thSample· 1mo ago

  Mehak, go to sleep after reading this.

  Bulb: the electric field spreads through the wire at close to the speed of light as soon as the switch closes, and every free electron along the entire wire starts drifting at once. The electrons already inside the filament are the ones that carry the current there. It's like a pipe completely full of water, you push at one end and water comes out of the other end immediately, even though each water molecule moves slowly.

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• [+][–]Siddharth RaoDropperSample· 1mo ago

  (1) $v_d = \dfrac{eE\tau}{m}$ and $E = V/L$. So $v_d \propto E \propto 1/L$ at fixed $V$. Doubling the length halves the drift velocity. It is not a pure material property, it depends on the field in the wire.

  (2) $I = nAev_d$ with $A=\pi r^2$. Same $I$, doubled radius means $A$ becomes 4 times, so $v_d$ becomes $1/4$. Not half. Radius is squared, that's the trick they want you to fall into.

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• [+][–]Tushar PawarDropperSample· 1mo ago

  Drift velocity is independent of length, it's a property of the material (depends on $n$, $\tau$, $m$). So case 1 is unchanged.

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  • [+][–]Siddharth RaoDropperSample· 1mo ago

    Not quite. The $\tau$, $m$ are material things, yes, but the electric field $E=V/L$ changes with length for the same voltage, and $v_d$ is proportional to $E$. If the current were fixed instead of V and the area same, then $v_d$ would be unchanged ($I = nAev_d$). Careful which quantity is held constant.

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    • [+][–]Tushar PawarDropperSample· 1mo ago

      That is the thing I missed, V fixed vs I fixed. Okay thanks.

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• [+][–]Zoya Khan12thSample· 1mo ago

  Mobility is the drift velocity per unit electric field, $\mu = v_d/E = \dfrac{e\tau}{m}$. Its SI unit is $\text{m}^2\text{V}^{-1}\text{s}^{-1}$. A good way to remember: bigger relaxation time $\tau$ (fewer collisions) means higher mobility. NCERT also links it to conductivity: $\sigma = ne\mu$ for electrons.

  And Mehak, I mean this kindly, ask yourself what the doubt is giving you at 1 am versus what sleep would. The doubt will still be here at 8. I know because I used to do the same.

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  • [+][–]Mehak AroraDropperSample· 1mo agoAuthor

    Thank you Zoya didi. I slept at 2 in the end 😅 but reading it again in the morning, all clear. 1/L and 1/4, noted.

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• [+][–]Kavya NaikDropperSample· 1mo ago

  Another quick exam trick: $v_d \propto I/(nA)$, so for the same current, a thinner wire has a larger drift velocity. And for different metals with the same current and area, the one with more free electrons per volume ($n$) has the smaller drift velocity.

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