MCQ
Three copper rods are subjected to different potential difference. Compare the drift speed of electrons through them. Assume that all $3$ are at the same temperature.
  Length Diameter Potential difference
$(A)$ $L$ $3d$ $V$
$(B)$ $2L$ $d$ $2V$
$(C)$ $3L$ $2d$ $2V$
  • $v_A = v_B > v_C$
  • B
    $v_A > v_B > v_C$
  • C
    $v_A < v_B < v_C$
  • D
    None of these

Answer

Correct option: A.
$v_A = v_B > v_C$
a
$\mathrm{i}=\mathrm{neAV}_{\mathrm{drift}}=\frac{\mathrm{V}}{\mathrm{R}}$

$\mathrm{R}=\frac{\rho \ell}{\mathrm{A}}=\frac{4 \rho \ell}{\pi \mathrm{d}^{2}}$

$\therefore {{\rm{V}}_{{\rm{drift}}}} = \frac{{\rm{V}}}{{{\rm{RneA}}}} = \frac{{\rm{V}}}{{\frac{{\rho \ell }}{{\rm{A}}} \times {\rm{neA}}}} = \frac{{\rm{V}}}{{\rho \ell {\rm{ne}}}} \propto \frac{{\rm{V}}}{\ell }$

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