Q: Current of 4.8 amperes is flowing through a conductor. The number of electrons per second will be

3 \times 10^{19}. Number of electrons per second n = i/e = 4.8 / (1.6 \times 10^{-19}) = 3 \times 10^{19}.

Q: Every atom makes one free electron in copper. If 1.1 ampere current is flowing in the wire of copper having 1 mm diameter, then the drift velocity (approx.) will be (Density of copper = 9 \times 10^{3}\ kg\ m^{-3} and atomic weight = 63)

0.1\ mm/sec. Electron density n = (6 \times 10^{23} / 63 \times 10^{-3}) \times 9 \times 10^{3} = 8.5 \times 10^{28}\ m^{-3}. With A = \pi (0.5 \times 10^{-3})^2, drift velocity v_d = i/(neA) = 1.1/(8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times 7.85 \times 10^{-7}) \approx 0.1\ mm/s.

Q: Which one is not the correct statement

1\ volt \times 1\ watt = 1\ H.P.. Volt \times watt is not a unit of power at all, so it cannot equal 1 H.P. The other three relations are dimensionally correct.

Q: Drift velocity v_d varies with the intensity of electric field as per the relation

v_d \propto E. From v_d = (e\tau/m)E, the drift velocity is directly proportional to the electric field, i.e. v_d \propto E.

Q: On increasing the temperature of a conductor, its resistance increases because

Relaxation time decreases. Resistance R = ml/(ne^{2}\tau A). Heating increases the vibration of lattice ions, so the relaxation time \tau decreases and R increases.

Question 1

Current of 4.8 amperes is flowing through a conductor. The number of electrons per second will be

Accepted Answer

3 	imes 10^{19}. Number of electrons per second n = i/e = 4.8 / (1.6 	imes 10^{-19}) = 3 	imes 10^{19}.

Question 2

Every atom makes one free electron in copper. If 1.1 ampere current is flowing in the wire of copper having 1 mm diameter, then the drift velocity (approx.) will be (Density of copper = 9 	imes 10^{3}\ kg\ m^{-3} and atomic weight = 63)

Accepted Answer

0.1\ mm/sec. Electron density n = (6 	imes 10^{23} / 63 	imes 10^{-3}) 	imes 9 	imes 10^{3} = 8.5 	imes 10^{28}\ m^{-3}. With A = \pi (0.5 	imes 10^{-3})^2, drift velocity v_d = i/(neA) = 1.1/(8.5 	imes 10^{28} 	imes 1.6 	imes 10^{-19} 	imes 7.85 	imes 10^{-7}) \approx 0.1\ mm/s.

Question 3

Which one is not the correct statement

Accepted Answer

1\ volt 	imes 1\ watt = 1\ H.P.. Volt 	imes watt is not a unit of power at all, so it cannot equal 1 H.P. The other three relations are dimensionally correct.

Question 4

The temperature coefficient of resistance for a wire is 0.00125\ /^{\circ}C. At 300 K its resistance is 1 ohm. The temperature at which the resistance becomes 2 ohm is

Accepted Answer

1127\ K. Using R_1/R_2 = (1 + \alpha t_1)/(1 + \alpha t_2) with t_1 = 27^{\circ}C: 1/2 = (1 + 0.00125 	imes 27)/(1 + 0.00125\,t_2), giving t_2 = 854^{\circ}C = 1127\ K.

Question 5

Ohm's law is true

Accepted Answer

For metallic conductors at low temperature. At high temperature the resistance of a metal changes appreciably and the V–i graph becomes non-linear; electrolytes and diodes are non-ohmic. So Ohm's law holds for metallic conductors at low temperature.

Question 6

The example for non-ohmic resistance is

Accepted Answer

Diode. A diode has a non-linear V–i characteristic, so it is a non-ohmic resistance.

Question 7

Drift velocity v_d varies with the intensity of electric field as per the relation

Accepted Answer

v_d \propto E. From v_d = (e	au/m)E, the drift velocity is directly proportional to the electric field, i.e. v_d \propto E.

Question 8

On increasing the temperature of a conductor, its resistance increases because

Accepted Answer

Relaxation time decreases. Resistance R = ml/(ne^{2}	au A). Heating increases the vibration of lattice ions, so the relaxation time 	au decreases and R increases.

Question 9

In a conductor 4 coulombs of charge flows for 2 seconds. The value of electric current will be

Accepted Answer

2 amperes. Current i = q/t = 4/2 = 2\ A.

Question 10

The specific resistance of a wire is \rho, its volume is 3\ m^{3} and its resistance is 3 ohms, then its length will be

Accepted Answer

\dfrac{3}{\sqrt{\rho}}. Volume V = lA = 3, so A = 3/l. Then R = \rho l/A = \rho l^{2}/3 = 3, giving l^{2} = 9/\rho and l = 3/\sqrt{\rho}.

Question 11

62.5 	imes 10^{18} electrons per second are flowing through a wire of area of cross-section 0.1\ m^{2}, the value of current flowing will be

Accepted Answer

10 A. i = ne = 62.5 	imes 10^{18} 	imes 1.6 	imes 10^{-19} = 10\ A. The area is not needed.

Question 12

A certain wire has a resistance R. The resistance of another wire identical with the first except having twice its diameter is

Accepted Answer

0.25\,R. R \propto 1/d^{2}. Doubling the diameter makes the area four times larger, so the resistance becomes R/4 = 0.25R.

Question 13

In hydrogen atom, the electron makes 6.6 	imes 10^{15} revolutions per second around the nucleus in an orbit of radius 0.5 	imes 10^{-10}\ m. It is equivalent to a current nearly

Accepted Answer

1\ mA. i = e 	imes f = 1.6 	imes 10^{-19} 	imes 6.6 	imes 10^{15} \approx 1.06 	imes 10^{-3}\ A \approx 1\ mA.

Question 14

A wire of length 5 m and radius 1 mm has a resistance of 1 ohm. What length of the wire of the same material at the same temperature and of radius 2 mm will also have a resistance of 1 ohm

Accepted Answer

20\ m. R \propto l/r^{2}. For R to stay the same when r doubles (area 	imes 4), the length must also become four times: l = 4 	imes 5 = 20\ m.

Question 15

When there is an electric current through a conducting wire along its length, then an electric field must exist

Accepted Answer

Inside the wire but parallel to it. The current is driven by the field inside the conductor, and it is directed along the length of the wire, i.e. inside the wire and parallel to it.

Question 16

Through a semiconductor, an electric current is due to drift of

Accepted Answer

Free electrons and holes. In a semiconductor both electrons (in the conduction band) and holes (in the valence band) act as charge carriers.

Question 17

In an electrolyte 3.2 	imes 10^{18} bivalent positive ions drift to the right per second while 3.6 	imes 10^{18} monovalent negative ions drift to the left per second. Then the current is

Accepted Answer

1.6 amp to the right. Positive ions moving right give 3.2 	imes 10^{18} 	imes 2e = 1.024\ A to the right; negative ions moving left also give a current 3.6 	imes 10^{18} 	imes e = 0.576\ A to the right. Total = 1.6\ A to the right.

Question 18

A metallic block has no potential difference applied across it, then the mean velocity of free electrons is (T = absolute temperature of the block)

Accepted Answer

Proportional to \sqrt{T}. With no external field the electrons have only random thermal motion, for which 	frac{1}{2}mv_{rms}^{2} = 	frac{3}{2}kT, so the speed is proportional to \sqrt{T}.

Question 19

The specific resistance of all metals is most affected by

Accepted Answer

Temperature. The specific resistance (resistivity) of a metal rises appreciably with temperature; the other factors have a negligible effect.

Question 20

The positive temperature coefficient of resistance is for

Accepted Answer

Copper. Metals such as copper have a positive temperature coefficient of resistance; carbon, semiconductors and electrolytes have negative coefficients.

Current Electricity — NEET Physics MCQs with Solutions

Subtopics

Sample questions with solutions