Tag: electric current, potential difference and resistance

Questions Related to electric current, potential difference and resistance

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 $E^2$

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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

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:

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

  1. $1\ mm/s$

  2. $2\ mm/s$

  3. $0.5\ mm/s$

  4. $0.36\ mm/s$

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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:- 

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

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

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

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

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

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Correct Option: D

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 ?

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

  1. $10^6$

  2. $10^7$

  3. $10^8$

  4. $10^9$

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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?

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

  1. $10^6$

  2. $10^7$

  3. $10^9$

  4. $10^8$

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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 $9000kgm^{2})$

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

  1. $0.74 mms^{-1}$

  2. $7.4 mms^{-1}$

  3. $74 mms^{-1}$

  4. $0.074 mms^{-1}$

Show answer
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  

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

  1. 1.0 mm/sec

  2. 1.0 m / sec

  3. 0.1 mm/sec

  4. 0.01 mm / sec

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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 

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

  1. v/4

  2. v/2

  3. 2v

  4. 4 v

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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} $