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Explanation:

An electric transformer is a device used in electrical systems to alter voltage levels in alternating current (AC). It operates based on electromagnetic induction and is primarily used to step up (increase) or step down (decrease) the voltage of AC. Transformers do not convert electrical energy into mechanical energy, change AC to DC, or store electricity.

• Transformers work with AC only.
• They step up or step down voltage levels.
• They cannot convert AC to DC or store electricity.

Therefore, the correct answer is Option 1.

Explanation:

When a metallic plate is getting heated, there can be multiple reasons contributing to this phenomenon. These reasons are related to the flow of current, presence of magnetic fields, and their interactions.​

(a) A direct current passing through the plate ⇒ True (Joule heating).

(b) An alternating current passing through the plate ⇒ True (Joule heating and eddy currents).

(c) The plate is placed in a time-varying magnetic field ⇒ True (induces eddy currents).

(d) The plate is placed in a space-varying magnetic field ⇒ False (space variation alone does not induce heating without motion or time variation).

Therefore, statements (a), (b), and (c) are correct.

Therefore, the correct answer is Option 2 (3 only).

Explanation:

Resistivity (ρ) of a material is a measure of how strongly it resists the flow of electric current. In metals like copper, resistivity increases with an increase in temperature due to enhanced scattering of electrons.

• At low temperatures, ρ is relatively small because electron scattering is minimal.
• As temperature rises, lattice vibrations increase, leading to higher electron scattering and thus higher ρ.
• For copper, the relationship between resistivity and temperature is typically linear over a wide range of temperatures.

Key points about the graph:

• Positive slope: 

The line should always go upwards, indicating that resistivity increases with temperature.

• Curved shape: 

The relationship is not linear but rather parabolic, meaning the rate of increase in resistivity gets slightly faster as temperature rises.

• Non-zero intercept: 

The line does not intersect the origin at (0,0) because copper has a specific resistivity even at 0°C.

Therefore, the correct answer is Option 4.

Calculation:

The total resistance in the circuit changes as R' is varied. The current I in the circuit is given by:

I = E / (r + (RR')/(R + R'))

For large values of R', the current decreases, and for small values of R', the current increases. However, since r is very small compared to R and R', the variation in current is limited when R' is varied.

The potential drop across AB is given by:

V_AB = I × R

Since R is fixed and I does not change significantly due to the small internal resistance r, V_AB remains nearly constant as R' is varied.

The current through R' is given by:

I_R' = V_AB / R'

Because V_AB is nearly constant, I_R' decreases as R' increases.

The inequality I ≥ E / (r + R) holds true because the total resistance (r + R + R') is always greater than (r + R).

Therefore, the correct answer is Option 3.

Concept:

In a pure resistive AC circuit, the following characteristics hold true:

• The current and voltage are in phase, which means their peaks, zero crossings, and troughs occur at the same times.
• There is no phase difference between the current and voltage.
• This behavior is distinct from inductive or capacitive circuits where phase differences occur.

Explanation:

In a resistive circuit:

• The voltage and current vary sinusoidally with time.
• Since the resistance does not introduce any phase shift, the voltage and current waveforms align perfectly.
• At any given instant, the voltage and current are proportional to each other as per Ohm's Law: V = IR.

Therefore, the correct answer is Option 4.

Calculation:

The time period (T) of a mass-spring system is given by the formula:

T = 2π √(m/k)

Here:

m = mass of the object

k = spring constant

The time period depends only on the mass (m) and spring constant (k). It is independent of the amplitude of oscillation.

If the amplitude of the oscillation is doubled, there is no change in the mass or spring constant. Hence, the time period (T) remains the same.

Therefore, the correct answer is Option 4.

Explanation:

Total internal reflection occurs when a light ray traveling from a medium with a higher refractive index to a medium with a lower refractive index is incident at an angle greater than the critical angle. The critical angle is the angle of incidence for which the angle of refraction is 90°.

∠AON does represents the critical angle for the air-glass interface.

The speed of light in glass is slower than that in air due to its higher refractive index.

If ∠AON is increased beyond the critical angle, total internal reflection will still occur.

∠AON is  necessarily equal to ∠BON due to law of reflection.

Therefore, the correct answer is Option 2.

Explanation:

The duration of daylight is longer than the time between sunrise and sunset due to the bending of light rays when they pass through the Earth's atmosphere. This phenomenon is explained by refraction of light.

• Reflection of light involves bouncing back of light rays from a surface, which does not apply here.
• Rectilinear propagation of light refers to light traveling in a straight line, which does not justify the observed phenomenon.
• Refraction of light occurs when light passes through mediums of different densities, causing it to bend. This bending allows the Sun to appear above the horizon even when it has technically set or before it has technically risen.
• Dispersion of light refers to the splitting of light into its constituent colors, which is unrelated to the duration of daylight.

Therefore, the correct answer is Option 3.

Explanation:

• (a) The image is real: A magnifying glass produces a virtual image when the object is inside the focal point. Hence, this statement is false.
• (b) The image is erect: A magnifying glass produces an erect image when the object is inside the focal point. Hence, this statement is true.
• (c) The image is larger than the object: When the object is inside the focal point, the magnifying glass produces a larger virtual image. Hence, this statement is true.
• (d) The lens is diverging: A magnifying glass is a convex (converging) lens. Hence, this statement is false.
• (e) The object is inside the focal point: For magnification, the object must be inside the focal point. Hence, this statement is true.
• (f) The image is necessarily outside the focal point: The image produced by the magnifying glass is virtual and appears on the same side as the object, not outside the focal point. Hence, this statement is false.

From the above analysis:

• Statements (b), (c), and (e) are true.
• Statements (a), (d), and (f) are false.

Therefore, the correct answer is Option 1.

The correct answer is (3)

Concave Refracting Surface — Clear Explanation

A concave refracting surface curves inward (like the inside of a bowl) as seen by the incoming light. Because of this inward curvature, the center of curvature—the center of the sphere of which the surface is a part—lies on the same side as the incident rays (i.e., in front of the surface from the light’s point of view).

• Inward curve: “Concave” means the surface bends toward the incoming medium, forming a hollow shape.
• Center location: The center of curvature is on the incident side since the surface is part of a sphere whose center lies in front of the surface for those rays.
• Position relative to rays: From the direction of incoming light, the center is before the surface, not behind it.

Sign-convention note (Cartesian): When light travels left → right and the surface is concave toward the left (incident side), the center lies to the left of the vertex, so the radius of curvature is taken as negative. This matches the idea that the center is on the same side as the incoming rays.

In summary, a concave refracting surface faces the incoming light with a hollowed shape, placing its center of curvature on the incident side, which is consistent with standard optical sign conventions.