Current and Drift Velocity Relation

Q.

What is the full form of M.S.E.B?

Q. A conducting wire of cross-sectional area $1c{m}^2$ has $3\times {10}^{23}$ number of charge carriers per unit volume. If wire carries a current of $24mA$, the drift speed of the carrier is ___________.

1. $5\times {10}^{-6}m{s}^{-1}$
2. $5\times {10}^{-2}m{s}^{-1}$
3. $0.5m{s}^{-1}$
4. $5\times {10}^{-3}m{s}^{-1}$

Q.

A current of $10A$ exists in a wire of cross-sectional area of $5m{m}^2$ with a drift velocity of $2\times {10}^{-3}m{s}^{-1}$. The number of free electrons in each cubic meter of the wire is ________

1. $1\times {10}^{23}$

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

3. $2\times {10}^{25}$

4. $625\times {10}^{25}$

Q. If the drift velocity of electrons in a conductor is V, then the drift velocity in another conductor of same material, but double the cross section and carrying half the current of first conductor is.

1. $\frac{V}{6}$
2. $V$
3. $\frac{V}{4}$
4. $\frac{V}{3}$

Q.

A current of 1.0 A exists in a copper wire of cross - section 1.0 $m{m}^2$. Assuming one free electron per atom calculate the drift speed of the free electrons in the wire. The density of copper is 9000 $kg{m}^{-3}$.

Q. { For a certain metal, v is five times the }v_0 and the }} maximum velocity of coming out photo electrons is }{8×10^6 . If }v=2v_0 , the maximum velocity of photo }} electrons will be

Q.

Two conducting wires X and Y of the same diameter but different materials are joined in series across a battery. If the number density of electrons in X is twice that in Y, find the ratio of the drift velocity of electrons in the two wires.

Q. The average time of motion of electrons between two successive collisions with fixed positive ions inside a conductor is called the time.

1. active
2. relaxation
3. collision
4. none of these

Q. A potential difference of V is applied at the ends of a copper wire of length $l$ and diameter $d$. On doubling only the length, the drift velocity:

1. Becomes twice.
2. Becomes half.
3. Does not change.
4. Becomes one fourth.

Q. In a wire of circular cross-section with radius r, free electrons travel with a drift velocity v, when a current i flows through the wire. What is the current in another wire of half the radius and of the some material when the drift velocity is 2v

1. 2i
2. i
3. $\frac{i}{2}$
4. $\frac{i}{4}$

Q. A wire has a non-uniform cross-sectional area as shown in figure. A steady current i flows through it. Which one of the following statement is correct

1. The drift speed decreases on moving from A to B
2. The drift speed of electron is constant
3. The drift speed increases on moving from A to B
4. The drift speed varies randomly

Q.

Two wires of the same material but of different radii carry the same current i. if the ratio of their radii is 4:2, then the corresponding ratio of their mean drift velocities will be.

Q.

plot a graph showing the variation of current density (j) versus the electric field (E) for two conductors of different materials. What information from this plot regarding the properties of the conducting material, can be obtained which can be used to select suitable materials for use in making (i) standard resistance and (ii) connecting wires in electric circuits?

Electron drift speed is estimated to be of the order of $mm{s}^{-1}$ Yet large current of the order of few amperes can be set up in the wire. Explain briefly.

Q. Consider a conductor of variable cross section in which current is flowing from cross section ‘1’ to ‘2’. Then which of the following is/are correct?

1. Current passing through both the cross sections is same
2. Current through ‘1’ is less than that through ‘2’
3. Drift velocity of electrons at ‘1’ is less than that at ‘2’
4. Drift velocity is same at both the cross sections.

Q. In a conductor, every atom contributes one free electron and the current flowing through it is $16A$. The area of cross section, length and density of this conductor are ${10}^{-6}{m}^2$, $1m$ and $5\times {10}^{3}kg/m^3$. The drift velocity of the electrons $($in $mm/s)$ is (Atomic weight = $60$, $N_A=6\times {10}^{23}$, $e=1.6\times {10}^{-19}C$

Q. A current passes through a wire of nonuniform cross-section. Which of the following quantities is independent of the cross-section?

1. The charge crossing in a given time interval.
2. Drift speed
3. Current density
4. None of these

Q. 1) Consider circuit in figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity?
$n=$ no of electron/volume $={10}^{29}/m^3$,
length of circuit $=10cm$,
cross-section $=A=(1mm{)}^2$



2) Electrons give up energy at the rate of $R{I}^2$ per second to the thermal energy. What time scale would one associate with energy $1.78\times {10}^{-17}J$?
$n=$ no of electron/volume $={10}^{29}/m^3$,
length of circuit $=10cm$,
cross-section $=A=(1mm{)}^2$

Q.

A proton and an α particle is accelerated through the same potential difference V. The wavelength associated with the two bear the ratio

1. 3: 2

2. 2√2: 1

3. 2: 1

4. 4: 1

Q. Ram knows that relation between current and drift velocity is $I=neA{V}_d$_.He is trying to solve a question where the current in a cylindrical conductor is to be calculated. The total number of electrons In the conductor is given as ${10}^{26}$, their drift speed is ${10}^{-2}cm/s$ and the cross- sectional area is $1m^2$ uniform throughout the conductor and its length is given as 2m
He writes this equation $I=neA{V}_d$
$={10}^{26}\times 1.6\times {10}^{-19}\times 1\times \frac{{10}^{-2}}{100}$
He gets a terribly wrong answer.
This is because

1. Ram is not using the correct value of the charge of an electron
2. Ram converted the units of speed into SI units wrongly
3. Ram doesn’t know that n stands for number of electrons per unit volume and not total number of electrons.
4. None of the above! Ram must have done some calculation mistake.

Q. We know that current $I=neA{V}_d$ where $V_d$ is the drift speed, A is the cross sectional area, e is the magnitude of charge on an electron and n is the number of free charge carriers in unit volume of a conductor. In a conductor of non-uniform cross-sectional area as shown

1: The current at P will be more than the current at Q
2: Because current is directly proportional to cross-sectional area so current increases as the cross sectional area increases

1. Statement 1 is correct, Statement 2 is the correct and Statement 2 is the correct explanation for statement 1
2. Statement 1 is correct, Statement 2 is the correct and Statement 2 is not the correct explanation of statement 1
3. Statement 1 is correct but Statement 2 is wrong
4. Both statements are wrong

Q. The number density of free electrons in a copper conductorestimated in Example 3.1 is 8.5 × 1028 m–3. How long does an electrontake to drift from one end of a wire 3.0 m long to its other end? Thearea of cross-section of the wire is 2.0 × 10–6 m2 and it is carrying acurrent of 3.0 A.

Q. Column I gives three physical quantities. Select the appropriate units for these from the choices given in column II. Some of the physical quantities may have more than one choice.

Column-I	Column - II
a) Capacitance	d) Ohm second
b) Inductance	e) Coulomb${}^2$ joule${}^{-1}$
c) Magnetic induction	f) Coulomb volt${}^{-1}$
	g) Newton (ampere/metre)${}^{-1}$
	h) Volt second (ampere)${}^{-1}$

1. a-h; b-d; c-e
2. a-e, f; b-d, h; c-g
3. a-e; b-g, h; c-g
4. a-e, f; b-d, h; c-d, e

Q. Answer the following questions: (a) A steady current flows in a metallic conductor of non-uniformcross-section. Which of these quantities is constant along theconductor: current, current density, electric field, drift speed? (b) Is Ohm’s law universally applicable for all conducting elements?If not, give examples of elements which do not obey Ohm’s law. (c) A low voltage supply from which one needs high currents musthave very low internal resistance. Why? (d) A high tension (HT) supply of, say, 6 kV must have a very largeinternal resistance. Why?

Q. A potential difference of V is applied at the ends of a copper wire of length $l$ and diameter $d$. On doubling only the length, the drift velocity:

1. Becomes twice.
2. Becomes half.
3. Does not change.
4. Becomes one fourth.

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

Consider the following circuit. At t = 0, the capacitor is uncharged and switch S is open. Choose the correct statement(s).

निम्नलिखित परिपथ पर विचार कीजिए। t = 0 पर, संधारित्र अनावेशित है तथा स्विच S खुला है। सही कथन/कथनों का चयन कीजिए।

1. Immediately after closing the switch S, current through battery is 7.5 A
   
   स्विच S को बंद करने के ठीक बाद, बैटरी से प्रवाहित धारा 7.5 A है
2. Immediately after closing the switch S, current through 2 Ω resistor will be 5 A
   
   स्विच S को बंद करने के ठीक बाद, 2 Ω के प्रतिरोधक से प्रवाहित धारा 5 A होगी
3. In steady state, charge on capacitor will be 40 μC
   
   स्थायी अवस्था में, संधारित्र पर आवेश 40 μC होगा
4. In steady state, current through 4 Ω resistor will be 10 A
   
   स्थायी अवस्था में, 4 Ω के प्रतिरोधक से प्रवाहित धारा 10 A होगी

Q. On what factors does the capacitance of a condutor depend?

Q.

A steady current flows in a metallic conductor of non-uniform cross section. The quantity/quantities constant along the length of the conductor is/are
[IIT-JEE 1997]

1. current, electric field and drift speed

2. drift speed only

3. current and drift speed

4. current only

Q. If the drift velocity of electrons in a conductor is V, then the drift velocity in another conductor of same material, but double the cross section and carrying half the current of first conductor is.

1. $V$
2. $\frac{V}{4}$
3. $\frac{V}{3}$
4. $\frac{V}{6}$

Q. A current of $1.0A$ exists in a copper wire of cross-section $1.0m{m}^2.$ Assuming one free electron per atom calculate the drift speed of the free electrons in the wire. The density of copper is $9000kg{m}^{-3}.$

Q. Work function for aluminium metal is 4.125 eV. For photo electric effect from aluminium metal, the cut off wavelength will be-

1. 200 nm
2. 300 nm
3. 150 nm
4. 420 nm