Tag: electric current, potential difference and resistance

Questions Related to electric current, potential difference and resistance

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?

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

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

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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?

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

  1. Drift velocity alone

  2. Thermal velocity alone

  3. Both drift velocity and thermal velocity

  4. Neither drift nor thermal velocity

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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:-

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

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

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

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

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

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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 105 m/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 $5.81 \times 10^{7} \Omega^{-1}$.$K =1.38 \times 10^{-23} JK^{-1}$).

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

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

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

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

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

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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.

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

  1. A

  2. B

  3. C

  4. D

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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

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

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

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

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

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

Show answer
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

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

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

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

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