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Why Do Stars Twinkle but Planets Usually Don’t?

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Stars appear to twinkle because their light passes through Earth’s atmosphere. Different layers of air have different temperatures and densities, so they continuously bend the starlight in slightly different directions. Stars are extremely far away and appear as point sources of light, so these changes make their brightness seem to fluctuate. Planets are much closer and appear as tiny disks rather than point sources. Light comes from many points across the disk, and the fluctuations from different parts tend to cancel each other out.
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Why Can’t an Object Reach the Speed of Light?

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According to Einstein’s special relativity , a massive object cannot reach the speed of light (c). As its velocity approaches (c), its relativistic energy increases enormously: E = γmc², where γ = 1/√(1 − v²/c²) When (v tends to c), γ → ∞, so an infinite amount of energy would be required to reach (c). Light can travel at (c) because photons have zero rest mass. Key idea : A massive object can approach the speed of light, but can never reach it.
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Why does a Capacitor Block DC but Allow AC?

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A capacitor stores electric charge and allows current only while its voltage is changing. ●DC: The voltage becomes constant after the capacitor is fully charged, so dV/dt = 0. Hence, current becomes zero. Therefore, a capacitor blocks DC. ●AC: The voltage continuously changes with time, so dV/dt ≠ 0. The capacitor continuously charges and discharges, allowing current to flow. Therefore, a capacitor allows AC.
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Why Does Temperature Remain Constant During a Phase Change?

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During a phase change, the heat supplied to a substance is used to overcome intermolecular forces and change its molecular arrangement, rather than increasing its temperature. This energy is called latent heat. For example, while ice melts at 0°C, its temperature remains 0°C until all the ice has melted.  So, even though temperature remains constant, internal energy changes.
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Entropy

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Entropy(S) is a thermodynamic state function that measures the degree of energy dispersal or randomness/disorder of a system. Unit:- J K-¹ For Specific entropy  Unit :- J Kg K-¹   ●                         dS=dQ/T For reversible process ds=0 For irreversible process ds>0 Examples :- ●Ice melting → entropy increases. ●Water evaporating → entropy increases. ●Gas expanding freely → entropy increases. ●Heat naturally flowing from hot to cold → total entropy increases.
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Electromagnetic induction.

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Electromagnetic induction is the phenomenon of production of an induced emf (electromotive force) in a closed circuit whenever the magnetic flux linked with the circuit changes. The induced emf is given by e=-dΦ/dt For a coil of N-turns e=-NdΦ/dt where magnetic flux is Φ=BAcosθ Lenz's law:- The induced current always flows in such a direction that it opposes the change in magnetic flux that produces it.
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What is resonance?

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Resonance is the phenomenon in which a system oscillates with maximum amplitude when the frequency of the external periodic force equals its natural frequency.
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