Current Electricity MCQ Test : 25 Interactive MHT-CET Physics Questions for 12th Grade

Current Electricity Mastery

25 Interactive MHT-CET Physics Questions for 12th Grade

Total Marks: 25

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1. In the absence of electric field across the conductor there is

Explanation: Without an applied electric field, although electrons move randomly due to thermal energy, their overall motion cancels out, resulting in no net flow of charge.

2. The average velocity of electrons in a conductor in the absence of electric field is

Explanation: In the absence of an electric field, the net drift velocity of electrons is nearly zero. However, if one considers the typical drift velocity when a field is applied, it is of the order of ${10}^{4}m/s$, which is very small compared to their random thermal speeds.

3. The direction of conventional current is in the

Explanation: By convention, current is defined as the flow of positive charge. This means it is opposite to the electron flow, in the direction of the electric field.

4. A charge of magnitude q flows through the conductor in time t. The current through the conductor is

Explanation: Current is defined as the rate of flow of charge. Therefore, if a charge $q$ passes through in time $t$, the current is $I=\frac{q}{t}$.

5. The velocity with which a free electron in a conductor gets drifted under the influence of the applied electric field is

Explanation: Under an electric field, the free electrons acquire a slow net movement called the drift velocity, even though they have high random thermal speeds.

6. The drift velocity of electrons in a conductor under the influence of electric field is

Explanation: In most conductors, the drift velocity under an applied electric field is very small, typically around ${10}^{-4}m/s$.

7. If A is the area of cross section of conductor, e be the charge on the electrons, n be the number of electrons per unit volume and J be the current density then drift velocity of electrons is

Explanation: The drift velocity is given by the relation $v_d=\frac{J}{ne}$, where $J$ is the current density, $n$ is the number of electrons per unit volume, and $e$ is the charge of an electron.

8. Under the action of electric field, a material is said to be a conductor of electricity if there is flow of

Explanation: In a conductor, the same type of charge carriers (electrons) flow uniformly (in fact, opposite to the electric field direction). Hence, the material conducts electricity when its like charges move collectively.

9. In conductors, current conduction takes place due to

Explanation: In metallic conductors, the electrons (which are negatively charged) drift opposite to the direction of the applied electric field, resulting in current conduction.

10. The direction of conventional current flowing through a metal due to applied potential difference or electric field is

Explanation: Conventional current is defined as the flow of positive charge. In a metal, this means the current flows in the direction of the electric field (from high potential to low potential), making both statements true.

11. A conductor of length l and area of cross section A has n number of electrons per unit volume of the conductor. The total charge carried by the conductor is

Explanation: The total number of electrons in the conductor is $n\times A\times l$, and each electron carries a charge $e$. Therefore, the total charge is $nAle$.

12. When a current I is set up in a wire of radius r, the drift velocity is $v_d$. If the same current is set up through a wire of radius 2r, the drift speed will be

Explanation: The cross-sectional area of a wire is proportional to $r^2$. Doubling the radius increases the area by a factor of 4. For the same current, the drift velocity is inversely proportional to the area; hence, the drift velocity becomes $\frac{1}{4}{v}_d$.

13. There is a current of 0.21 A in a copper wire of area of cross section ${10}^{-6}{m}^2$. If the number of electrons per $m^3$ is $8.4\times {10}^{28}$ then the drift velocity is (with $e=1.6\times {10}^{-19}$ C)

Explanation: Using the formula $I=nAe{v}_d$, the drift velocity is calculated as $$v_d=\frac{I}{nAe}=\frac{0.21}{8.4\times {10}^{28}\times {10}^{-6}\times 1.6\times {10}^{-19}}\approx 1.562\times {10}^{-5}m/s.$$

14. The speed at which current travels in a conductor is nearly

Explanation: Although the drift velocity of electrons is very small, the signal (electromagnetic wave) travels nearly at the speed of light in a conductor – approximately $3\times {10}^{8}m/s$.

15. An electron in the hydrogen atom circles around the proton with a speed of $2.18\times {10}^{6}m/s$ in an orbit of radius 0.53 Å. The equivalent current is

Explanation: The period of revolution is $$T=\frac{2\pi r}{v}.$$ With $r=0.53\text{Å}=0.53\times {10}^{-10}m$, we have $$T\approx \frac{2\pi (0.53\times {10}^{-10})}{2.18\times {10}^6}\approx 1.53\times {10}^{-16}s.$$ The equivalent current is $$I=\frac{e}{T}\approx \frac{1.6\times {10}^{-19}}{1.53\times {10}^{-16}}\approx 1.048\times {10}^{-3}A.$$

16. A potential difference is applied across the ends of a metallic wire. If the potential difference is doubled, the drift velocity will be

Explanation: The drift velocity is directly proportional to the applied electric field, and the electric field is proportional to the potential difference. Doubling the potential difference doubles the drift velocity.

17. In your city electricity cost 40 paise per kWh. You pay for

Explanation: Electricity bills are calculated based on the energy consumed (measured in kilowatt-hours), not simply charge, power, or current.

18. The relation between current density, conductivity and electric intensity is

Explanation: Ohm’s law in its microscopic form states that the current density $J$ is directly proportional to the electric field $E$, with the constant of proportionality being the conductivity $\sigma$, i.e., $J=\sigma E$.

19. The average time interval between two successive collisions of electrons with the vibrating atoms is called

Explanation: The relaxation time is defined as the average time between successive collisions of conduction electrons with the lattice ions in a conductor.

20. Resistivity of a material of a conductor is inversely proportional to

Explanation: The resistivity $\rho$ of a conductor is given by $$\rho =\frac{m}{n{e}^2\tau },$$ where $n$ is the number density and $\tau$ is the relaxation time. Hence, resistivity is inversely proportional to both.

21. The relaxation time

Explanation: As temperature increases, the lattice vibrations become more intense, which leads to more frequent collisions and thus a decrease in the relaxation time.

22. In the absence of electric field, the mean velocity of free electrons in a conductor at absolute temperature T is

Explanation: While electrons possess high random thermal speeds, their average drift velocity (net velocity) in the absence of an electric field is zero.

23. The velocity of charge carriers of current (about 1 A) in a metal under normal conditions is of the order of

Explanation: Although the electromagnetic signal propagates very fast, the actual drift velocity of electrons in a conductor is extremely slow – typically just a fraction of a millimetre per second.

24. The quantity in electricity analogous to temperature is

Explanation: In many analogies between electrical and thermal systems, the electric potential (voltage) is analogous to temperature, as both drive a flow – of charge and heat, respectively.

25. Increase in which property of free electrons causes increase in the resistance of a conductor with rise in temperature?

Explanation: In metals, as temperature rises, increased lattice vibrations lead to a decrease in the relaxation time (not an increase). The other properties remain nearly constant. Hence, none of the listed properties increase in a way that causes the resistance to rise.

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