Tag: electric current, potential difference and resistance

Questions Related to electric current, potential difference and resistance

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

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

  1. increase

  2. decrrease

  3. fluctuate

  4. remains constant

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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 :-

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

  1. increases two times

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

  3. does not change

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

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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

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

  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

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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

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

  1. v is doubled

  2. l is doubled

  3. The diameter of the wire is doubled

  4. The temperature of the wire is doubled

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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.

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

  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

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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 

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

  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

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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 . .

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

  1. 1:2

  2. 2:1

  3. 1:4

  4. 4:1

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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 .....

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

  1. three times

  2. doubled

  3. half

  4. four times

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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

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

  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

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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.

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

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

  2. $10^3$m/s

  3. $1$m/s

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

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Correct Option: D
Explanation:

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