$(A)$ The drift velocity $v_d$ is given by the formula $v_d = \frac{eE\tau}{m}$, where $E = \frac{V}{L}$.Thus, $v_d = \frac{eV\tau}{mL}$.Since all rod

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$(A)$ The drift velocity $v_d$ is given by the formula $v_d = \frac{eE\tau}{m}$, where $E = \frac{V}{L}$.Thus, $v_d = \frac{eV\tau}{mL}$.Since all rods are made of copper and are at the same temperature, the relaxation time $\tau$ and the mass of electron $m$ are constant.Therefore, $v_d \propto \frac{V}{L}$.For rod $(A)$: $v_A \propto \frac{V}{L} = 1 \cdot (V/L)$.For rod $(B)$: $v_B \propto \frac{2V}{2L} = 1 \cdot (V/L)$.For rod $(C)$: $v_C \propto \frac{2V}{3L} = 0.67 \cdot (V/L)$.Comparing the values, we get $v_A = v_B > v_C$.

Class 12 Physics Current Electricity Current Density, Drift Velocity and Mobility

Medium

Three copper rods are subjected to different potential differences. Compare the drift speed of electrons through them. Assume that all $3$ are at the same temperature.
Rod Length,Diameter,Potential Difference
$(A)$ $L, 3d, V$
$(B)$ $2L, d, 2V$
$(C)$ $3L, 2d, 2V$

A
$v_A = v_B > v_C$
B
$v_A > v_B > v_C$
C
$v_A < v_B < v_C$
D
None of these

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Current Electricity

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Current Density, Drift Velocity and Mobility

Assertion: Free electrons always keep on moving in a conductor,even then no magnetic force acts on them in a magnetic field unless a current is passed through it.
Reason: The average velocity of free electrons is zero.

EasyAIIMS 2016

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$A$ conductor wire having $10^{29}$ free electrons $/ m^{3}$ carries a current of $20 \,A$. If the cross-section of the wire is $1 \,mm^{2}$, then the drift velocity of electrons will be. $\left(e=1.6 \times 10^{-19} \,C\right)$

MediumKCET 2011

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$A$ current of $5\, A$ passes through a copper conductor (resistivity $= 1.7 \times 10^{-8}\, \Omega \, m$) of radius of cross-section $5\, mm$. Find the mobility of the charges if their drift velocity is $1.1 \times 10^{-3}\, m/s$.

MediumJEE MAIN 2019

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The drift velocity of electrons in a current-carrying wire of radius $r$ is $v$. If we want a drift velocity of $2v$ in a wire of the same material but with half the radius,what current must be passed through it?

Easy

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$A$ current flows in a wire of circular cross-section with the free electrons travelling with a mean drift velocity $\vec v$. If an equal current flows in a wire of twice the radius,the new mean drift velocity is:

Difficult

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Rod	Length,Diameter,Potential Difference
$(A)$	$L, 3d, V$
$(B)$	$2L, d, 2V$
$(C)$	$3L, 2d, 2V$

Three copper rods are subjected to different potential differences. Compare the drift speed of electrons through them. Assume that all $3$ are at the same temperature.RodLength,Diameter,Potential Difference$(A)$$L, 3d, V$$(B)$$2L, d, 2V$$(C)$$3L, 2d, 2V$

Similar Questions

Assertion: Free electrons always keep on moving in a conductor,even then no magnetic force acts on them in a magnetic field unless a current is passed through it.Reason: The average velocity of free electrons is zero.

$A$ conductor wire having $10^{29}$ free electrons $/ m^{3}$ carries a current of $20 \,A$. If the cross-section of the wire is $1 \,mm^{2}$, then the drift velocity of electrons will be. $\left(e=1.6 \times 10^{-19} \,C\right)$

$A$ current of $5\, A$ passes through a copper conductor (resistivity $= 1.7 \times 10^{-8}\, \Omega \, m$) of radius of cross-section $5\, mm$. Find the mobility of the charges if their drift velocity is $1.1 \times 10^{-3}\, m/s$.

The drift velocity of electrons in a current-carrying wire of radius $r$ is $v$. If we want a drift velocity of $2v$ in a wire of the same material but with half the radius,what current must be passed through it?

$A$ current flows in a wire of circular cross-section with the free electrons travelling with a mean drift velocity $\vec v$. If an equal current flows in a wire of twice the radius,the new mean drift velocity is:

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Three copper rods are subjected to different potential differences. Compare the drift speed of electrons through them. Assume that all $3$ are at the same temperature.
Rod Length,Diameter,Potential Difference
$(A)$ $L, 3d, V$
$(B)$ $2L, d, 2V$
$(C)$ $3L, 2d, 2V$

Assertion: Free electrons always keep on moving in a conductor,even then no magnetic force acts on them in a magnetic field unless a current is passed through it.
Reason: The average velocity of free electrons is zero.