Tag: physics

Questions Related to physics

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

physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

  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.

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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.

physics electric current drift velocity and mobility drift speed drift velocity & mobility

  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

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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

physics electric current drift velocity and mobility drift speed drift velocity & mobility

  1. $K _1 < K _2$

  2. $K _1 = K _2$

  3. $K _1 > K _2$

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

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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:

physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

  1. directly proportional to electron density

  2. directly proportional to relaxation time

  3. inversely proportional to electron density

  4. inversely proportional to relaxation time

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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?

physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

  1. $1.25\,m/s$

  2. $125000\,m/s$

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

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

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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 $=60$)

physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

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

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

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

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

Show answer
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:

physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

  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 $E^2$

Show answer
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 $Cu=63$] 

physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

  1. True

  2. False

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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.

physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

  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 $3 : 1$.

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

physics electric current drift velocity and mobility drift speed drift velocity & mobility

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

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

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

  4. $ 10^{-3}$

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Correct Option: A
Explanation:

Length ,$d=2m$

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