The drift velocity of electrons in a conducting wire connected to a cell is $\mathrm{V}_{\mathrm{d}}$. If…

The drift velocity of electrons in a conducting wire connected to a cell is $\mathrm{V}_{\mathrm{d}}$. If the length of the wire is doubled and area of cross-section is halved then the drift velocity of electrons becomes.
  1. $\mathrm{V}_{\mathrm{d}}$
  2. $\frac{V_d}{2}$
  3. $2 \mathrm{~V}_{\mathrm{d}}$
  4. $4 V_d$

Solution

Drift velocity is given by $\begin{aligned} & \mathrm{v}_{\mathrm{d}}=\frac{\mathrm{I}}{\mathrm{neA}} \\ & \mathrm{v}_{\mathrm{d}}=\frac{\mathrm{V}}{\mathrm{neAR}} \quad(\therefore \mathrm{V}=\mathrm{IR}) \\ & =\frac{\mathrm{VA}}{\mathrm{neA} \rho \ell} \quad \because \mathrm{R}=\frac{\rho \ell}{\mathrm{A}} \\ & =\frac{\mathrm{V}}{\mathrm{ne} \rho \ell} \\ & \mathrm{V}_{\mathrm{d}}^{\prime}=\frac{\mathrm{V}}{\mathrm{ne} 2 \ell}=\frac{\mathrm{V}_{\mathrm{d}}}{2} \end{aligned}$

Asked in: AP EAMCET 2023 (15 May Shift 2)

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