CUET UG Physics Booster Test – 2 Fundamentals of Electric Curren

Electric current is associated with the net flow of charge through a given area. NCERT explains that charges in motion constitute electric current, and the direction of current depends on the algebraic contribution of moving charges. Both positive and negative charges can move in different directions depending on the conducting medium. For example, in electrolytic solutions, both positive and negative ions may move. If the net amount of charge flowing in the assumed forward direction becomes negative, it means the actual current is opposite to the assumed direction. Statement 1 is correct because charge carriers of both signs may move. Statement 3 is also correct because a negative value of net forward charge indicates backward current. Statement 2 is incorrect because positive charges flowing forward and negative charges flowing backward contribute in the same conventional current direction. Statement 4 is incorrect because negative charge carriers strongly affect net current.

The net charge flowing through a cross-section must be calculated by considering the sign of each charge carrier. Here, 5×10¹⁸ electrons move forward. Since each electron has charge −e, their contribution is −5×10¹⁸ × 1.6×10⁻¹⁹ C = −0.80 C. Also, 2×10¹⁸ positive monovalent ions move forward. Since each ion carries charge +e, their contribution is +2×10¹⁸ × 1.6×10⁻¹⁹ C = +0.32 C. Therefore, the net forward charge is q = −0.80 C + 0.32 C = −0.48 C. The negative sign indicates that the net charge flow is opposite to the positive conventional direction. NCERT stresses that current is based on net charge flow, not merely the number of particles. Therefore, the correct net forward charge is −0.48 C.

For a steady current, the amount of net charge q crossing any area of a conductor must be directly proportional to the time interval t. This means q = It, where I is constant. Therefore, the quotient q/t gives the same value for any chosen time interval. This is the NCERT definition of steady current. If instead q is proportional to t², then q/t becomes proportional to t. Hence the current does not remain constant with time; it changes as time changes. Such a current is not steady but varying. A cell-driven clock or a torch is a common example of a device in which charges flow steadily in a circuit. Therefore, the statement that q ∝ t² represents steady current is incorrect. The correct test for steady current is constant rate of charge flow, not merely continuous charge movement.

Electric current is defined as the rate of net charge flow through a cross-sectional area. In this question, the positive charge flowing forward in time t is αt. Since positive charge contributes positively in the forward direction, its contribution is +αt. The negative charge flowing forward is βt. Since negative charges carry negative charge, their contribution to net forward charge is −βt. Therefore, the net forward charge is q = αt − βt = α − β t. The current is I = q/t = αt − βt / t = α − β. Since α and β are constants, the current is steady. This follows directly from the NCERT idea that the algebraic amount of charge crossing a surface per unit time gives electric current. Thus, the correct expression is α − β.

For a varying current, average current over a finite time interval does not give the exact value of current at a particular instant. NCERT defines instantaneous current as the limiting value of ΔQ/Δt as Δt tends to zero. Mathematically, this is written as I = dQ/dt. Here, the charge flowing through the cross-section is Q(t) = at² + bt + c. To find the instantaneous current, differentiate Q(t) with respect to time t. The derivative of at² is 2at, the derivative of bt is b, and the derivative of the constant c is zero. Therefore, I = dQ/dt = 2at + b. This expression gives the current at any instant t. It is not obtained by simply dividing total charge by total time, because that would give an average value, not instantaneous current.

For a steady current, the charge flowing through a cross-section is proportional to time, so the quotient ∆Q/∆t remains constant. However, in a varying current, the rate of charge flow changes from instant to instant. Therefore, if we take a large time interval ∆t, the ratio ∆Q/∆t gives only the average current over that interval and not the exact current at a particular moment. NCERT defines instantaneous current using the limiting process in which ∆t tends to zero. Mathematically, instantaneous current is written as I = lim ∆t→0 ∆Q/∆t = dQ/dt. This definition helps us find the current at a specific instant when charge flow is continuously changing. Thus, the limit is necessary because a macroscopic time interval cannot capture the exact instantaneous rate of charge flow.

The SI unit of electric current is the ampere. In NCERT Physics, the ampere is associated with the magnetic effects of electric current. Moving charges produce magnetic effects, and historically the unit ampere was defined using the magnetic force between current-carrying conductors. The second blank asks about the scale of current in a nervous system impulse. Biological currents are very small compared with household appliances or lightning. NCERT mentions that nerve currents are generally of the order of microamperes. This is much smaller than the current drawn by domestic appliances, which is usually of the order of amperes. Lightning, on the other hand, may involve currents of tens of thousands of amperes. Therefore, the correct completion is magnetic effects and microamperes.

NCERT highlights that electric currents occur over a very wide range of magnitudes. A lightning strike is an intense natural electric discharge and may carry current of the order of tens of thousands of amperes, which is represented approximately as 10⁴ A. A typical domestic appliance such as a bulb, fan, or small electrical device generally draws current of the order of one ampere, written as 10⁰ A. Human nerve impulses involve the movement of ions across nerve membranes and are associated with very small currents. These are usually of the order of microamperes, represented as 10⁻⁶ A. A very small biological current is also described as being in the microampere range. Therefore, the correct matching is 1-b, 2-a, 3-c, and 4-d. This matching is based on the standard NCERT order-of-magnitude comparison for electric currents.

NCERT explains that free charged particles occur naturally in some physical situations and are also present in conducting materials. In the upper strata of the atmosphere, called the ionosphere, charged particles such as ions and electrons exist and can move under electric fields. In isolated atoms and molecules, however, negatively charged electrons are bound to positively charged nuclei by electrostatic attraction. Such bound electrons are not generally free to move across macroscopic distances. In metals, the atoms are closely packed and some valence electrons are no longer attached to individual atoms. These electrons behave as practically free charge carriers within the metallic bulk and are responsible for conduction. Statement 4 is incorrect because a small electric field does not guarantee extraction of electrons from all materials. Bound electrons may remain attached to their atoms or molecules. Therefore, statements 1, 2, and 3 are correct.

In atoms and isolated molecules, electrons are bound to nuclei by electrostatic attraction. In many materials, the valence electrons remain attached to their respective atoms or molecules and are not free to move throughout the bulk matter. NCERT distinguishes such bound charges from free charge carriers found in metals or electrolytic solutions. When an electric field is applied to a material with tightly bound electrons, those electrons do not accelerate freely across macroscopic distances to form a steady current. At most, they may undergo slight displacement within the atom or molecule, but they remain attached to their nuclei. A steady electric current requires mobile charge carriers that can drift under the action of an electric field. Since tightly bound valence electrons are not mobile, the material does not behave like a metallic conductor. Therefore, the correct statement is that the electrons will not accelerate freely and will remain attached to their respective nuclei.

In a metallic conductor, atoms are arranged in a crystal lattice. The positively charged ions occupy fixed positions and form the stationary background of the metal. Some of the valence electrons become practically free and are not attached to individual atoms. NCERT explains that these free electrons move randomly due to thermal motion when no electric field is present. When an electric field is applied, the electrons acquire a small drift velocity opposite to the direction of the electric field. This directed motion of free electrons constitutes electric current. The lattice ions do not move through the conductor and therefore do not contribute to the macroscopic current. Thermal motion alone also cannot produce a net current because it is random. Thus, current in metallic conductors is carried by the free electrons moving through a fixed positive ion background.

Electrolytic solutions conduct electricity through the motion of ions. Unlike metallic conductors, where free electrons move through a fixed positive ion lattice, electrolytes contain both positively charged ions (cations) and negatively charged ions (anions) that are free to move in the liquid medium. When an electric field is applied, cations drift towards the negative electrode while anions drift towards the positive electrode. Both types of ions contribute to the electric current. NCERT emphasizes that conduction in electrolytes differs fundamentally from conduction in metals because the charge carriers are ions rather than free electrons. Since both positive and negative charges are mobile, the total current is the result of contributions from both types of ions. Therefore, option B correctly describes electrolytic conduction.

Free electrons in a metal are in constant random thermal motion. They frequently collide with the fixed positive ions of the lattice. After each collision, the direction of motion changes randomly, and there is no preferred direction of movement. Because equal numbers of electrons move in all directions on average, the vector sum of their velocities becomes zero. NCERT explains that although electrons possess large thermal speeds, their random motion does not result in a net transfer of charge across a cross-section. Therefore, no measurable steady current is produced in the absence of an external electric field. A steady current requires a directed drift motion of charge carriers. Hence the statement that random thermal motion itself produces a measurable steady current is incorrect.

In a metallic conductor with no applied electric field, free electrons move randomly due to thermal energy. At any instant, some electrons move in one direction while others move in opposite directions. Because there is no preferred direction, the vector sum of all electron velocities tends to cancel out. When this sum is divided by the total number of electrons, the average velocity becomes zero. NCERT uses this concept to explain why thermal motion does not produce electric current. Although individual electrons have significant thermal speeds, the overall average velocity remains zero because the motions are equally distributed in all directions. Since electric current depends on net charge transport, zero average velocity means no net current flows through the conductor.

When opposite charges are placed at the ends of a metallic cylinder, an electric field is established inside the conductor. According to the convention used in NCERT, the electric field direction is from the positive charge towards the negative charge. Free electrons present in the conductor experience an electric force given by F = qE. Since the electron charge is negative, the force acts opposite to the electric field direction. Consequently, electrons drift towards the positively charged disc. This drift motion constitutes electric current in the conductor. The direction of conventional current is opposite to the electron drift direction. Therefore, the electron drift is opposite to the electric field and directed towards the +Q disc.

When finite charges +Q and -Q are placed at the ends of a metallic cylinder, an electric field is produced inside the conductor. The electric field is directed from the positive charge towards the negative charge. Since electrons carry negative charge, the force on them acts opposite to the electric field. Therefore, electrons accelerate towards the +Q boundary. This directed motion of electrons constitutes electric current. However, the current is not permanent because the boundary charges are finite. As electrons move, they neutralise the positive charge and reduce the electric field. Once the charges are neutralised, the electric field becomes zero and the directed acceleration stops. Hence this current is transient, not steady. The applied electric field acts on free electrons also, not only on positive ions. Therefore, statements 1 and 3 are correct.

When discs carrying charges +Q and -Q are attached to the ends of a metallic cylinder, an electric field is created inside the conductor. The direction of this field is conventionally from +Q to -Q. The free electrons in the metal experience force opposite to this field and begin to drift towards the positive disc. Their accumulation near the positive disc neutralises the positive charge. As this process continues, the finite boundary charges are gradually neutralised. Once complete neutralisation is achieved, the electric field inside the conductor becomes zero. Without an electric field, there is no directed drift of electrons and hence no current. Since there is no continuous replenishment mechanism, the current exists only for a short duration. Therefore, the correct matching is 1-b, 2-c, 3-a, and 4-d.

Electric current is defined as the rate of flow of charge through a cross-section. For a current I flowing for a time t, the charge transferred is given by Q = It. Here, the transient current is 2.0 A and the time is 1.5 milliseconds. Since SI units must be used, 1.5 milliseconds = 1.5 × 10⁻³ seconds. Therefore, Q = 2.0 × 1.5 × 10⁻³ = 3.0 × 10⁻³ C. The unit verification is also correct because ampere is coulomb per second, so A × s = C. This charge represents the amount transferred during the transient current and hence the absolute magnitude of the initial charge on one disc required for neutralisation. Therefore, the correct answer is 3.0 × 10⁻³ C.

A metallic cylinder with only finite charges at its ends can produce current only for a short time. The free electrons move under the electric field and gradually neutralise the end charges. Once the end charges are neutralised, the electric field disappears and current stops. To maintain continuous current, fresh charges must be supplied at the ends of the conductor. The neutralised charges must be continuously replenished by an external mechanism so that the potential difference does not vanish. This keeps a steady electric field inside the conductor. NCERT explains that practical devices like cells and batteries perform this function in electric circuits. They maintain a potential difference and allow continuous charge flow. Therefore, statements 1, 2, and 4 are correct. Statement 3 is incorrect because if the electric field falls to zero, directed drift stops and the current cannot remain steady.

Electric current is defined as the rate of flow of charge. In SI units, current is measured in amperes, where 1 ampere = 1 coulomb per second. The battery replenishes charge at a rate of k coulombs per minute. Since one minute contains 60 seconds, this rate must be converted into coulombs per second before writing current in amperes. Therefore, I = k/60 coulombs per second. Since coulomb per second is ampere, the steady current maintained is I = k/60 A. This calculation follows directly from the NCERT definition I = Q/t. The battery maintains the potential difference and replenishes charge continuously, allowing steady current to flow through the conductor.