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Drift speed - class-XII

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A charged particle having drift velocity of $7.5\times 10^{-4}m$ $s^{-1}$ in electric field of $3\times 10^{-10}$V $m^{-1}$, mobility is?

  1. $6.5\times 10^6m^2V^{-1}s^{-1}$

  2. $2.5\times 10^6m^2V^{-1}s^{-1}$

  3. $2.5\times 10^4m^2V^{-1}s^{-1}$

  4. $6.5\times 10^4m^2V^{-1}s^{-1}$


Correct Option: B
Explanation:

Given:
$V _d=7.5 \times 10^{-4}$
$E=3 \times 10^{-10}$
Mobility of charged particle
$\mu =\dfrac{|v _d|}{E}=\dfrac{7.5\times 10^{-4}}{3\times 10^{-10}}=2.5\times 10^6m^2V^{-1}s^{-1}$.

Which of the following characteristics of electrons determines the current in a conductor?

  1. Drift velocity alone

  2. Thermal velocity alone

  3. Both drift velocity and thermal velocity

  4. Neither drift nor thermal velocity


Correct Option: A
Explanation:

A. Drift velocity only.


The current in a conductor,

$I= neA V _{d}$
    where, $n=$ no. of free charge density
                $A=$ cross-sectional area of conductor
                 $V _{d}=$ Drift velocity
From the above, Drift velocity is only responsible for the current in a conductor.

When current flows through a conductor, then the order of drift velocity of electrons will be:-

  1. $10^{10} cms^{-1}$

  2. $10^{-2} cms^{-1}$

  3. $10^{4} cms^{-1}$

  4. $10^{-1} cms^{-1}$


Correct Option: B
Explanation:

The drift velocity of electrons in a conductor is of the order of $10^{−4} m/s. It is very small compared to the thermal speed which is of the order of 10m/s.

The answer is $10^{-2}$

Potential difference of $100 V$ is applied to the ends of a copper wire one metre long. Find the ratio of average drift velocity and thermal velocity of electrons at $27^\circ C$. (Consider there is one conduction electron per atom. The density of copper is $9.0 \times 10^3$; Atomic mass of copper is $63.5 g$.
$N _A = 6.0 \times 10^{23}$ per gram-mole, conductivity of copper is $5.81 \times 10^{7} \Omega^{-1}$.$K =1.38 \times 10^{-23} JK^{-1}$).

  1. $3.67 \times 10^{-6}$

  2. $4.3 \times 10^{-6}$

  3. $6 \times 10^{-5}$

  4. $5.6 \times 10^{-6}$


Correct Option: A

Assertion: When a straight wire is bent to form L-shape, its resistance increases.
Reason: Electrons take longer time to travel along a bent wire, as compared to travel along a straight wire.

  1. A

  2. B

  3. C

  4. D


Correct Option: D

When the current in a wire is 1A, the drift velocity is $1.2\times 10^{-4}ms^{-1}$. The drift velocity when current becomes 5 A is

  1. $1.2\times 10^{-4}ms^{-1}$

  2. $3.6\times 10^{-4}ms^{-1}$

  3. $6\times 10^{-4}ms^{-1}$

  4. $4.8\times 10^{-4}ms^{-1}$


Correct Option: C
Explanation:

Given
Initial current through the wire is $I = 1A$
Initial drift velocity is, $v _d = 1.2 \times 10^{-4} ms^{-1}$
Increased current is, $I' = 5A$
The current, I through the wire is given by
$I = \mu _e.e.A.v _d$
where, $\mu _e$ is the free electron density, e is the charge on electron, A is the area of cross section of the wire and v_d is the drift velocity of electrons. 
Since,  the free electron density, the charge on electron and the area of cross section of the wire are constant, hence
$I \propto v _d$.................(1)
Now, current through the wire is increased to 5 A, if the new drift velocity of electrons is $v' _d$ then
$I' \propto v' _d$................(2)


From (1) and (2), we can write

$\dfrac{v' _d}{v _d} = \dfrac{I'}{I}$

$v' _d = \dfrac{I'}{I} v _d$

$v' _d = \dfrac{5}{1} 1.2 \times 10^{-4}$ 

$v' _d = 6 \times 10^{-4} ms^{-1}$ 

A charge $A$ of $+3 \ mC$ is placed at $k=0$ and a charge $B$ of $-5 \ mC$ at $k=40 \ mm.$ Where a third charge q be placed on the axis such that it experiences no force is

  1. $1.6 \times 10^{-1} \ m$ from $B$ outside

  2. $2.52 \times 10^{-1} \ m$ from $B$ outside

  3. $4.42 \times 10^{-1} \ m$ from $B$ outside

  4. $8.24 \times 10^{-1} \ m$ from $B$ outside.


Correct Option: A

In conducting wire of radius $5 \, mm$, resistivity $\rho = 1.1 \times 10^{-8} \Omega/m$ and current of $5 A$ is flowing. Drift velocity of free electron is $1.1 \times 10^{-3} \, m/s$ find out mobility of free electron.

  1. $1.57 \, m^2$ volt/sec

  2. $1.25 \, m^2$ volt/sec

  3. $1.2 \, m^2$ volt/sec

  4. $2 \, m^2$ volt/sec


Correct Option: A
Explanation:

$V _d = \mu E = \mu \dfrac{V}{\ell}$
$V _d = \dfrac{\mu. I R}{\ell} \dfrac{\mu. I _{\rho} \ell}{A \ell} = \dfrac{\mu . I _{\rho}}{A}$
$\mu = \dfrac{V _d . A}{I _{\rho}} = \dfrac{1.1 \times 10^{-3} \times \lambda \times 25 \times 10^{-6}}{5 \times 1.1 \times 10^{-8}}$
$\mu = 1.57 \,  m^2 $ volt/sec.

A current passes through a resistor. If K$ _1$ and K$ _2$ represent the average kinetic energy of the conduction electrons and the metal ions respectively then

  1. $K _1 < K _2$

  2. $K _1 = K _2$

  3. $K _1 > K _2$

  4. $\text{Any of these three may occur}$


Correct Option: C
Explanation:

Considering law of conservation of momentum ,electrons possess drift velocity which is greater than velocity of ions.  Thus $K _1>K _2$. hence correct option is option C.

Mobility of free electrons in a conductor is:

  1. directly proportional to electron density

  2. directly proportional to relaxation time

  3. inversely proportional to electron density

  4. inversely proportional to relaxation time


Correct Option: B
Explanation:

Mobility of free electrons, $\mu = \dfrac{q\tau}{m}$        

$\implies$    $\mu \propto \tau$               $(\because q$ and $m$ are constants $)$
Hence mobility of free electrons in a conductor is directly proportional to relaxation time.

A 2-ampere current flows in a conductor which has $1 \times {10^{24}}$ free electrons per meter. What is their average drift velocity?

  1. $1.25\,m/s$

  2. $125000\,m/s$

  3. $3 \times {10^8}\,m/s$

  4. $1.25 \times {10^{ - 5}}\,m/s$


Correct Option: A
Explanation:

We know 
$I = \eta eAV$
$2 = 1 \times {10^{24}} \times 1.6 \times {10^{ - 24}} \times 1 \times v$
$\boxed{v = 1.25\,m/s}$

An electric current of $16A$ exists in a metal wire of cross section ${ 10 }^{ -6 }{ m }^{ 2 }$ and length $1m$. Assuming one free electron per atom. The drift speed of the free electrons in the wire will be:
(Density of metal $=5\times { 10 }^{  }kg/{ m }^{ 3 }$, atomic weight $=60$)

  1. $5\times { 10 }^{ -3 }m/s$

  2. $2\times { 10 }^{ -3 }m/s$

  3. $4\times { 10 }^{ -3 }m/s$

  4. $7.5\times { 10 }^{ -3 }m/s$


Correct Option: B
Explanation:

We know,


$I=neAv _d$
      where n=electron density,
                  e=electronic charge
                  A= cross section area
                  $v _d$=drift velocity

But, $n=\dfrac{\rho}{Atm. \ Wt}\times N _A$

And $v _d=\dfrac{I}{neA}$

So, $v _d=\dfrac{16\times 60}{5\times 10^4\times N _A\times 1.6\times 10^{-19}\times 10^{-6}}$

Taking $N _A=6\times 10^{23}$

$v _d=\dfrac{120\times 10^{-2}}{6}=2\times 10^{-3}$

Drift velocity $v _a$ varies with the intensity of elastic filed as per the relation:

  1. $v _a$ is directly proportionate to E

  2. $v _a$ is inversely proportionate to E

  3. $v _a$ is constant

  4. $v _a$ is directly proportional to $E^2$


Correct Option: A
Explanation:
Drift velocity can be defined as the average velocity of electrons flowing inside a conductor under the influence of an electric field, which is responsible for the potential difference along the length of the conductor.

The relation between the electric field and potential is given by the following relation:

$ E=V/L$

Or,

$E = - \dfrac{dV}{dR} $


The electric potential changes along the distance in an electric field.

So, in a conductor with a potential difference between its ends, the electrons flow under the influence of this electric field. And the electric force is responsible for the acceleration of electrons and give then a drift velocity.

A copper wire of cross-section $2\ {mm}^{2}$ carries a current of $30\ A$. Calculate the root mean square velocity (thermal velocity) of free electrons at $27^oC$. Also ${v} _{d}$ is very small compared to it.
[Data given: ${ \rho  } _{ { C } _{ 0 } }=8.9\ gm/cc$, Boltzmann constant $(k)=1.38\times {10}^{23}J/K$
${m} _{0}=9.1\times {10}^{-31}kg.{N} _{A}=6.023\times {10}^{23}$ atomic weight of $Cu=63$] 

  1. True

  2. False


Correct Option: A

Two wires $X$ and $Y$ have the same resistivity but their cross-sectional areas are in the ratio $2 : 3$ and lengths in the ratio $1 : 2$. They are first connected in series and then the parallel to a d.c. source. Find the ratio of their drift speeds of the electrons in the two wires for the two cases.

  1. Series $6 : 2$, Parallel $2 : 1$.

  2. Series $3 : 2$, Parallel $2 : 1$.

  3. Series $5 : 2$, Parallel $2 : 1$.

  4. Series $3 : 2$, Parallel $3 : 1$.


Correct Option: B

The drift velocity of the electron in a copper wire of length 2m under the application of a potential difference of 200 V is $0.5 ms^{-1}$.Their mobility is (in $m^{-2} V^{-1} s^{-1}$)

  1. $5 \times 10^{-3}$

  2. $2.5 \times 10^{-2}$

  3. $5 \times 10^{2}$

  4. $ 10^{-3}$


Correct Option: A
Explanation:

Length ,$d=2m$

potential difference ,$V=200V$
Drift velocity, $v _d=0.5 m/s$
mobility ,$\mu=\dfrac{v _d}{E}$
$=\dfrac{v _d .d}{V}$
$=\dfrac{0.5}{200} \times 2$
$=\dfrac{0.5}{100}=5 \times 10^{-3} m^2 V^{-1} s^{-1}$

Current is flowing with a current density $J=480\ amp/cm^{2}$ in a copper wire. Assuming that each copper atom contribution one free electron and gives that  Avogadro number$=6.0\times 10^{23}\ atoms/mole$  Density of copper $=9.0\ g/cm^{3}$ .Atomic weight of copper $=64\ g/mole$ Electronic charge $=1.6\times 10^{-19}$ coulomb. The drift velocity of electrons is:

  1. $1\ mm/s$

  2. $2\ mm/s$

  3. $0.5\ mm/s$

  4. $0.36\ mm/s$


Correct Option: D
Explanation:

Given that,

 Current density $J=480\,amp/c{{m}^{2}}$

Avogadro number $N=6.0\times {{10}^{23}}\,atoms/mole$

Density of copper $\rho =9.0\,g/c{{m}^{3}}$
Atomic weight of copper $m=64\,g/mole$

Electronic charge $e=1.6\times {{10}^{-19}}\,coulomb$

We know that

Current density $J=\dfrac{I}{A}$

Now, the drift velocity is

${{v} _{d}}=\dfrac{J}{ne}....(I)$

We know that,

$n={{N} _{A}}\times \dfrac{1}{m}\times \rho $

Now, put the value of n in equation (I)

  $ {{v} _{d}}=\dfrac{Jm}{{{N} _{A}}e\rho } $

 $ {{v} _{d}}=\dfrac{480\times 64}{6.0\times {{10}^{23}}\times 1.6\times {{10}^{-19}}\times 9} $

 $ {{v} _{d}}=\dfrac{30720}{86.4\times {{10}^{4}}} $

 $ {{v} _{d}}=355.5\times {{10}^{-4}}\,cm/s $

 $ {{v} _{d}}=0.36\,mm/s $

Hence, the drift velocity is $0.36\,mm/s$ 

Assume that each atom of copper contributes one free electron. The density of copper is $9g cm^{-3}$ and atomic weight of copper is $63$. If the current flowing through a copper wire of $1mm$ diameter is $1.1 $ ampere, the drift velocity of electrons will be:- 

  1. $0.01 mm s^{-1}$

  2. $0.02 mm s^{-1}$

  3. $0.2 mm s^{-1}$

  4. $0.1 mm s^{-1}$


Correct Option: D

Find the time an electron takes to drift from one end of a uniform wire $3m$ long to its other end if the wire is $2$ x ${ 10 }^{ -6 }{ m }^{ 2 }$ in cross section and carries a current $3A$.The density of free electrons in a copper conductor is $8.5$ x ${ 10 }^{ 28 }{ m }^{ 3 }$.

  1. $2.7$ x ${ 10 }^{ 4 }s$

  2. $1.1$ x ${ 10 }^{ -4 }s$

  3. $0.9$ x ${ 10 }^{ -4 }s$

  4. $1.414$ x ${ 10 }^{ 4 }s$


Correct Option: A

How many electrons should be removed from a coil of mass 1.6 gram so that it may float in an electric field of intensity $10^9 NC^-1$ directed upwards ?

  1. $10^6$

  2. $10^7$

  3. $10^8$

  4. $10^9$


Correct Option: C

How many electrons should be removed from a coin of mass 1.6 gram, so that it may float in an electric field of intensity $10^9 NC^-1$ directed upwards?

  1. $10^6$

  2. $10^7$

  3. $10^9$

  4. $10^8$


Correct Option: A

A current of $1.0A$ exists in a copper wire of cross-section $1.0mm^2$.Assuming one free electron per atom

Calculate drift speed of the free electron in the wire _______(the density of copper is $9000kgm^{2})$

  1. $0.74 mms^{-1}$

  2. $7.4 mms^{-1}$

  3. $74 mms^{-1}$

  4. $0.074 mms^{-1}$


Correct Option: D
Explanation:

$i=ne AV _d$
$n=\dfrac{6\times 10^{23}\times 9000}{63.5\times 10^{-3}}$


$=8.5\times 10^{28}m^{-3}$

Hence $vd = \dfrac{i}{neA}$
$=\dfrac{1}{8.2\times 10^{28}\times 1.602\times 10^{19}\times 10^{-3}}$
$=7.4\times 10^{-5}m/s$
$0.07mm/s$

There is a current of 1.344 amp in a copper wire whose area of cross-section normal to the length of the wire is $ 1 mm^2 $. If the number of free electrons per $ cm^3  is 8.4 \times 10^22 $, then the drift velocity would be  

  1. 1.0 mm/sec

  2. 1.0 m / sec

  3. 0.1 mm/sec

  4. 0.01 mm / sec


Correct Option: A
Explanation:

Given that,

Current $I=1.344\,A$

Area of cross-section, $A=1\,m{{m}^{2}}=0.01\,c{{m}^{2}}$

Number of free electrons, $n=8.4\times {{10}^{22}}$

Charge on electron $e=1.6\times {{10}^{-19}}\,$

Drift velocity is given by

$ {{v} _{d}}=\dfrac{i}{nAe} $

$ =\dfrac{1.344}{8.4\times {{10}^{22}}\times 0.01\times 1.6\times {{10}^{-19}}} $

$ =\dfrac{1.344}{{{10}^{3}}\times 0.1344} $

$ ={{10}^{-2}}\,cm/\sec  $

$ =1\,mm/\sec  $

A current I flows through a uniform wire of diameter d when the electron drift velocity is V .The same current will flow through a wire of diameter d/2  made of the same material if the drift velocity of the electrons is 

  1. v/4

  2. v/2

  3. 2v

  4. 4 v


Correct Option: A
Explanation:

The relation between current and drift velocity is

$ I=neA{{v} _{d}} $

$ {{v} _{d}}=\dfrac{I}{neA} $

$ {{v} _{d}}=\dfrac{I}{ne\pi {{r}^{2}}} $

According to given data,

$ v _{d}^{'}=\dfrac{1}{ne\pi {{(2r)}^{2}}} $

$ v _{d}^{'}=\dfrac{1}{4}\dfrac{1}{ne\pi {{r}^{2}}} $

$ {{v} _{d}}'=\dfrac{{{v} _{d}}}{4} $

There is a current of 40 amperes in a wire of $10^{-16}m^{2}$ area of cross-section. If the number of free electrons per $m^{3}$ is $10^{29}$, then the drift velocity will be:

  1. $1.25\times 10^{3}$ m/s

  2. $2.50\times 10^{3}m/s$

  3. $2.0\times 10^{6}m/s$

  4. $25\times 10^{6}m/s$


Correct Option: D
Explanation:

If L is the length of wire so velocity is given by $v=\dfrac{L}{t}$

Total number of free electrons in the wire, $Q=nqLA$

Current,

$ I=\dfrac{Q}{t} $

$ I=\dfrac{nqLA}{t} $

$ I=nqvA $

$ v=\dfrac{I}{nqA} $

Where, n is the number of electron, $n={{10}^{29}}$

q is the charge of an electron, $q=1.6\times {{10}^{-19\,}}C$

A is area, $A={{10}^{-16}}\,{{m}^{2}}$

I is current, $I=40\,A$

So, drift velocity,

$ v=\dfrac{40}{{{10}^{29}}\times 1.6\times {{10}^{-19}}\times {{10}^{-16}}} $

$ v=25\times {{10}^{6}}\,m/s $

A potential difference $V$ is applied to a copper wire of length $l$ and thickness $d$. If $V$ is doubled, the drift velocity:

  1. Is doubled

  2. Is halved

  3. Remain same

  4. Becomes zero


Correct Option: A
Explanation:

In the first case, $E= V/l$ so $E$ is directly proportional to $V$ so $E$ will be doubled. Since $V= IR$ so, $E= IR/l$ so Resistance is doubled and $Vd$ is directly proportional to $E$ so $Vd$ is doubled. So in the case, everything is doubled.

The number of free electrons per $10$ mm ordinary copper wire is about $2\times 10^{21}$. The average drift speed of the electrons is $0.25$ mm current flowing is:

  1. $0.8$ A

  2. $8$ A

  3. $80$ A

  4. $5$ A


Correct Option: B
Explanation:

Given,

Number of electron, $n=2\times {{10}^{21}}$

Average drift speed, $0.25\,mm/s$

$ Q=ne $

$ Q=2\times {{10}^{21}}\times 1.6\times {{10}^{-19}} $

$ Q=320\,C $

Since,

$ s=\dfrac{D}{T} $

$ T=\dfrac{D}{s} $

$ T=\dfrac{10}{0.25}=40 $

So, current

$ I=\dfrac{Q}{T} $

$ I=\dfrac{320}{40} $

$ I=8\,A $

There is current of 40 amperes in a wire of $10^{-6}m^{2}$ area of cross -section. If the number of free electrons per $m^{3}$ is $10^{29}$, then the drift velocity will be 

  1. $1.25\times 10^{3}m/s$

  2. $2.50\times 10^{-3}m/s$

  3. $25.0\times 10^{-3}m/s$

  4. $250\times 10^{-3}m/s$


Correct Option: A

Drift speed of conduction electrons in the wire is

  1. $5.5cm/s$

  2. $0.55 mm/s$

  3. $0.22 mm/s$

  4. $1.1 mm/s$


Correct Option: B

In a wire of cross section radius r, free electrons travel with drift velocity V when a current a $I$ flows throught the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2V$ ?

  1. $2I$

  2. $I$

  3. $I/2$

  4. $I/4$


Correct Option: B

Which of the following quantities do not change when an ohmic resistor connected to a battery is heated due to the current?

  1. drift speed

  2. resistivity

  3. resistance

  4. number of free electrons


Correct Option: D
Explanation:

We know, for a conductor carrying current,
Drift speed $= neI =ne \dfrac{V}{R}$
Resistivity $= \dfrac {RA}{L}$
where,
$n$ is no. of electrons, 
$e$  is charge on electrons,
$V$  is applied voltage,
$R$  is resistance and 
$A$  and $L$  are area of cross-section and length of resistor.
From above equations it is clear that drift speed, resistivityand resistance of resistor will be affected due to heating of resistor

The drift of the electrons in a copper-wire of length 2 m under the application of potential difference of $ 200 V is 0.5 ms^{-1} $ . their mobility is $ (inm^2V^{-1}s^{-1} ) $

  1. $ 2.5 \times 10^{-3} $

  2. $ 2.5 \times 10^{-2} $

  3. $ 5 \times 10^{2} $

  4. $ 5 \times 10^{-3} $


Correct Option: D

In semiconductor the concentrations of electrons and holes are $8 \times 10 ^ { 18 } / \mathrm { m } ^ { 3 }$and $5 \times 10 ^ { 8 } / \mathrm { m } ^ { 3 }$ respectively.If the mobilities of electrons and holes are 2.3$\mathrm { m } ^ { 2 } / \mathrm { Vs }$ and 0.01$\mathrm { m } ^ { 2 } / \mathrm { Vs }$ respectively then semi conductor is

  1. N-type with resistivity $0.34 \Omega - \mathrm { m }$

  2. P-type with resistivity $0.34 \Omega - \mathrm { m }$

  3. N-type with resistivity $0.034 \Omega - \mathrm { m }$

  4. P-type with resistivity $3.4 \Omega - \mathrm { m }$


Correct Option: C

The mean free path of electrons in a metal is $44 \times 10 ^ { - 8 } \mathrm { m }$ . Theelectric field which can give on an average 2$e \mathrm { V }$ energy to an electron in the metal will be in units of VIm 

  1. $8 \times 10 ^ { 7 }$

  2. $5 \times 10 ^ { - 11 }$

  3. $8 \times 10 ^ { - 11 }$

  4. $5 \times 10 ^ { 7 }$


Correct Option: D

When 3 V potential difference is applied a wire of length 0.1 m. having resistivity $1.6 \times 10^{-5}$ $\Omega m$, the electrons started moving. If the electron density in the wire is $6 \times 10^{10} m^{-1}$, the drift speed of electrons is  

  1. $1.94 \times 10^{-6}\ ms^{-1}$

  2. $1.94 \times 10^{-5}\ ms^{-1}$

  3. $1.94 \times 10^{-8}\ ms^{-1}$

  4. $1.94 \times 10^{-7}\ ms^{-1}$


Correct Option: C

The drift velocity of free electron in a metal wire of a given potential gradient along it is $ V _d $ if this potential gradient is doubled the new drift velocity will be 

  1. $ V _d $

  2. $ 2V _d $

  3. $ \frac {V _d}{2} $

  4. $4V _d $


Correct Option: B

Unit of mobility :

  1. $Cskg$

  2. $m^2 V^{-1} s^{-1}$

  3. $Cskg^{-1}$

  4. $m^2 V^{-1} s$


Correct Option: B
Explanation:

Mobility    $\mu = \dfrac{v _d}{E}$

Unit of  $v _d $ is  $m/s$  and  that of  $E$ is $V/m$
So, its unit is    $m^2 V^{-1}s^{-1}$

When a potential difference $V $  is applied across a conductor at a temperature $T,$  the drift velocity of electrons is proportional to

  1. $\sqrt{V}$

  2. $V$

  3. $\sqrt{T}$

  4. $T$


Correct Option: B
Explanation:

We know that Drift velocity $v _d = \displaystyle \dfrac{eE}{m} \tau = \dfrac{e}{m} \tau \left ( \dfrac{V}{l} \right ) $ ($\because E = \dfrac{V}{l})$

so for a particular conductor of a particular length the drift velocity will directly depend upon voltage
Hence $v _d \propto V$. option B is correct.

If temperature is decreased, then relaxation time of electrons in metals will

  1. increase

  2. decrrease

  3. fluctuate

  4. remains constant


Correct Option: A
Explanation:

With decrease in temperature, resistance of metal conductor decreases. But  $R \propto  \dfrac{1}{\tau}$, therefore time of relation $\tau$ increases. that's why the correct answer is option A.

A potential difference V is applied across a copper wire of diameter d and length L. when only d is doubled, the drift velocity :-

  1. increases two times

  2. decreases $\displaystyle \frac{1}{2}$ times

  3. does not change

  4. decreases $\displaystyle \frac{1}{4}$ times


Correct Option: C
Explanation:

Drift velocity $\displaystyle v _d=\frac{I}{neA}=\frac{V/R}{neA}=\frac{V}{neA(\frac{\rho L}{A})}=\frac{V}{ne\rho L}$
Thus, drift velocity is independent of diameter so it does not change.

The drift velocity of electrons in a conducting wire is of the order of $1:mm/s$, yet the bulb glows very quickly after the switch is put on because

  1. the random speed of electrons is very high of the order of $10^{-6}m/s$

  2. the electrons transfer their energy very quickly through collision.

  3. electric field is set up in the wire very quickly, producing a current through each cross section, almost intantaneously

  4. All the above


Correct Option: C
Explanation:

Drift velocity $v _d= \frac{eEt}{m}$ so drift velocity is directly proportional  to the electric filed. When switch is on, the filed is quick set up wire  and produce current through wire instantaneously.   

A potential difference v exists between the ends of a metal wire of length l. The drift velocity will be doubled if

  1. v is doubled

  2. l is doubled

  3. The diameter of the wire is doubled

  4. The temperature of the wire is doubled


Correct Option: A
Explanation:

The drift velocity is $v _d=\frac{eVt}{2ml}$
The relaxation time t changes with change of temperature. Actually it decreases with rise of temperature. Thus at a given temperature drift velocity  is directly proportional to the potential difference, inversely proportional to length and is independent of cross-sectional area.
So when drift velocity is doubled , V becomes double and l is half.

Assertion : A current flows in a conductor only when there is an electric field within the conductor.


Reason : The drift velocity of electron in presence of electric field decreases.

  1. Both (A) and (R) are true and (R) is the correct explanation of A

  2. Both (A) and (R) are true but (R) is not the correct explanation of A.

  3. (A) is true but (R) is false

  4. (A) is false but (R) is true


Correct Option: C
Explanation:

Current flows when there in P.D.

The presence of P.D implies the presence of Electric field. 
Drift velocity $\propto$ Electric field.

 The electron drift speed is small and the charge of the electron is also small but still, we obtain large current in a conductor. This is due to 

  1. the conducting property of the conductor

  2. the resistance of the conductor is small

  3. the electron number density of the conductor is small

  4. the electron number density of the conductor is enormous


Correct Option: D
Explanation:

Current in the conductor $I = An e v _d$

where $n$ is the number density of free electrons, $v _d$ is the drift velocity of electrons, $e$ is its charge and $A$ is the cross-section area of conductor.
Conductors have very large number density of free electrons, nearly $10^{28}$ $cm^{-3}$, which conduct electric current in the conductor. Thus inspite of having small drift velocity and electronic charge, we obtain large current in the conductor.

Two wires, each of radius r, but of different materials are connected together end to end. If the densities of charge carriers in the two wires are in the ratio 1:4, the ratio of the drift velocity of electrons in the two wires will be . .

  1. 1:2

  2. 2:1

  3. 1:4

  4. 4:1


Correct Option: D
Explanation:

We know that drift velocity is inversely proportional to density of charge carriers.


Hence, ratio of drift velocity is $4:1$.

Answer-(D)

The drift velocity of an electron is doubled if the applied electric field across the conductor is .....

  1. three times

  2. doubled

  3. half

  4. four times


Correct Option: B
Explanation:

The flow of current current is nothing but drift velocity of electrons. Since current is directly proportional to voltage applied, drift velocity of electrons will also be directly proportional to the voltage applied. And it follows Ohm's law as V = I/R. So, if voltage is doubled, current is doubled and hence the drift velocity is doubled.

When there is an electric current through a conducting wire along its length then an electric field must exist

  1. inside the wire but normal to it

  2. inside the wire but parallel to it

  3. outside the wire but normal to it

  4. outside the wire but parallel to it


Correct Option: B
Explanation:

As current is flowing through it , it means charges are flowing along its length therefore heir must be some electric field parallel to the length of the wire. Hence correct option is B.

Copper contains $8.4\times 10^{28}$ free electrons$/m^3$. A copper wire of cross-sectional area $7.4\times 10^{-7}m^2$ carries a current of $1$A. The electron drift speed is approximately.

  1. $10^{-8}$m/s

  2. $10^3$m/s

  3. $1$m/s

  4. $10^{-3}$m/s


Correct Option: D
Explanation:

$v=\dfrac{I}{ne}=\dfrac{1}{7.4\times 10^{-7}}\times 8.4\times 10^{28}$
$=\dfrac{10^{-2}}{8.4\times 1.6\times 7.4}=10^-3$.

Drift velocity varies with the intensity of electric field as per the relation

  1. ${v} _{d}\propto E$

  2. ${v} _{d}\propto \cfrac{1}{E}$

  3. ${v} _{d}=$ constant

  4. ${v} _{d}\propto {E}^{2}$


Correct Option: A
Explanation:

Current , $I$ = $neAv _{d} $

Current density , $J$ = $\frac{I}{A}$ = $nev _{d} $
Also , current density $J$ is related to electric field $E$
by the relation 
$J = \sigma E$
Therefore , 
$nev _{d}$ = $J = \sigma E$
Hence , $v _{d}  \alpha E$ .

a current 10 ampere is maintained in a conductor of cross section of $ 10^{-4}m^2 $. if the electron density is $ 9 \times 10^{28} m^{-3} $ , what is the drift velocity of free electrons?

  1. $ 6.9 \times 10^{-6} ms^{-1} $

  2. $ 6.9 \times 10^{-4} ms^{-1} $

  3. $ 6.9 \times 10^{5} ms^{-1} $

  4. none of thses


Correct Option: A

The relaxation time $(t)$ is the:

  1. Time taken by an electron to drift from one end of a conductor to the other.

  2. Time taken by an electron to travel unit distance through the conductor.

  3. The time between two successive collisions of a free electron with the atoms of the metal.

  4. Time for which a free electron is subjected to the electric field.


Correct Option: C
Explanation:

Relaxation time is the average times between two successive collision between the free electrons and the atoms(kernel) of atoms .


It is denoted by $\tau$.

Answer-(C)

The drift velocity of free electrons in a conductor is $v$, when a current. $I$ is flowing in it if both the radius and current are doubled, then drift velocity will be.

  1. $V/4$

  2. $V/2$

  3. $2V$

  4. $4V$


Correct Option: B

The ratio of the drifty velocity $v _d$ and r.m.s. velocity of electrons is

  1. $10^{-10}$

  2. $10^{-5}$

  3. $10^{-3}$

  4. $10^{-6}$


Correct Option: A
Explanation:

We assume the electrons in a copper wire of radius 0.815 mm and carrying current 1 A at room temp 300 K.
Drift velocity , $v _d=\frac{I}{neA}=\frac{1}{(8.47\times 10^{28})\times (1.6\times 10^{-19})\times \pi\times (0.815\times 10^{-3} )^2 } \sim 3.45\times 10^{-5} m/s$
and $v _{rms}=\sqrt{\frac{3k _BT}{m}}=\sqrt{\frac{3\times (1.38\times 10^{-23})\times 300}{9.1\times 10^{-31}}}=1.17\times 10^5  m/s $
thus, $\frac{v _d}{v _{rms}}=10^{-10}$

When no current is passed through a conductor

  1. the free electrons do not move

  2. the average speed of a free electron over a large period of time is zero

  3. the average velocity of a free electron over a large period of time is zero

  4. the average of the velocities of all the free electrons at an instant is zero


Correct Option: C,D
Explanation:

When no current pass through the conductor i.e. when there is no electric field is applied to the conductor, each electron moves along a straight path at constant speeds and collide with the lattice ions(positive). With each collision the direction of electrons is changing randomly. The resulting path of any electron over along period of time, covering many collisions is a random sequence of straight segments. Due to this, the average number of electrons crossing any small area is nearly equal(in any direction). Thus the average displacement of electrons along any direction during any long period of time is also zero. Hence, the average velocity component in any direction is zero.

In metals, the time of relaxation of electrons

  1. increases with increasing temperature

  2. decreases with increasing temperature

  3. does not depend on temperature

  4. changes suddenly at $400 K$


Correct Option: B
Explanation:
Resistivity of a material is given by $\displaystyle\rho=\dfrac{m}{ne^2\tau}$ 

where $m=$mass of electron, $ n=$ electron density, $e=$ electronic charge and $\tau=$ relaxation time.

Resistance $\displaystyle R=\dfrac{\rho l}{A}=\dfrac{ml}{ne^2\tau A}$ or $\displaystyle R \propto \dfrac{1}{\tau}$

Since in metals Resistance increases with temperature so the relaxation of electrons decreases with increasing temperature.

A wire   whose cross - sectional area is increasing linearly from  its cone end to the other,  is connected  across a battery of V  volts.  Which of the  following quantities remain constant in the  wire ? 

  1. drift speed

  2. current density

  3. electric current

  4. electric field


Correct Option: C

A current of $5A$ passes through a copper conductor $(resistivity=1.7\times10^{-8}\Omega m$) of radius of cross-section $5mm$. Find the mobility of the charges if their drift velocity is $1.1\times 10^{-3}m/s$

  1. $1.3m^2/Vs$

  2. $1.5m^2/Vs$

  3. $1.8m^2/Vs$

  4. $1.0m^2/Vs$


Correct Option: D
Explanation:

$\mu=\dfrac{V _d}{E}$     $E=\rho J$


$=\dfrac{1.1\times 10^{-3}}{1.7\times 10^{-8}\times \dfrac{5}{\pi \times 25\times 10^{-6}}}$

$=\dfrac{1.1\times 10^{-3}\times \pi \times 25\times10^{-6}}{1.7 \times 10^{-8} \times5}\approx 1.01m^2/Vs$

Charge carriers, each of charge q, move along a wire of fixed length. The number density of the
charge carriers in the wire is n.
What is also required, for this wire, to determine the average drift velocity of the charge carriers in
terms of n and q?

  1. current per unit of cross-sectional area

  2. potential difference per unit of length

  3. resistance and cross-sectional area

  4. resistivity and length


Correct Option: A
Explanation:

We know that 

$I = nqAv _d$
$\implies v _d=  \dfrac{I}{A}\times \dfrac{1}{nq} $
we have the value of $n$ and $q$, 
So, to find the value of $v _d$ we require $\dfrac{I}{A}$ i.e. current per unit cross-sectional area.

A current I flows through a uniform wire of diameter d when the mean electron drift velocity is
V. The same current will flow through a wire of diameter d/2 made of the same material if the
mean drift velocity of the electron is:

  1. v/4

  2. v/2

  3. 2v

  4. 4v


Correct Option: D
Explanation:

Let I be the current flow through wire. 

Let V be the drift velocity of wire which has diameter d. 
Let A be the area of wire. 
Consider a wire of same material but diameter is half
Therefore, Area =$\dfrac{A}{4}$
Since, $I=NeAV$
N is same for both wire because both of them made of same material. 
$I _{1}=I _{2}$
$NeA _{1}V _{1}=NeA _{2}V _{2}$
$AV=\dfrac{A}{4}V _2$
$V _{2}=4V$


The electric current in a wire may be calculated using the equation $I=Anvq$.
Which statement is not correct?

  1. n is the number of charge carriers per unit volume of the wire

  2. nA is the number of charge carriers per unit length of the wire

  3. q is the charge of each charge carrier

  4. v is the velocity of each charge carrier


Correct Option: D
Explanation:

Given that,

Electric current in the wire  , $I=Anvq$

Here $A$ is the cross-section of wire 
$n$ is the number of charge carriers per unit volume of wire
$v $ is  drift velocity of charge carriers 
$q$ is the charge of each charge carier 

Hence incorrect statement is $(D)$

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