Three copper rods are subjected to different potential difference… - Vidyadip

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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