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

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.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a charge to experience no force, the electric fields from the two charges must cancel out. Since the charges have opposite signs, the null point must be outside the region between them, closer to the smaller magnitude charge (3 mC). Solving k(q1)/x^2 = k(q2)/(x+d)^2 leads to the position 1.6 x 10^-1 m from the -5 mC charge.

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

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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. $\text{Any of these three may occur}$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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. $1.25 \times {10^{ - 5}}\,m/s$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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. $7.5\times { 10 }^{ -3 }m/s$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $N _A=6\times 10^{23}$

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

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

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 $E^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics electric current, potential difference and resistance drift velocity and mobility drift speed drift velocity & mobility

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 $3 : 1$.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Drift velocity v_d = I / (neA). In series, current I is the same, so v_d is inversely proportional to A. In parallel, voltage V is the same, so I = V/R, where R = rho*L/A. Thus v_d = V / (ne*rho*L). Calculating these ratios yields 3:2 for series and 2:1 for parallel.

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

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}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Length ,$d=2m$

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