NCERT Solutions

If one solves all these questions then it is great but it is not something mandatory. Practicing these questions helps students develop a strong understanding of Coulomb's law, electric charges, the superposition principle, and electric field lines. Even practicing a significant portion helps in boosting exam confidence and helps students to score high in the examination.

The NCERT textbook is good to start with as it introduces students to the basic concepts and explains these topics to provide conceptual clarity. However, the exemplar focuses on reasoning, challenging multiple-choice questions and numerical problems. The exemplar is like the supplement that boosts students' grasp on these concepts given in the NCERT textbook through reasoning, multiple-choice and numerical problems.

students can check the table for the principal values for all ITFs below;

To understand this, Assume you have a bucket that has infinite number of apples and if your mother asks "give me the apple". How will you figure out which one is "The Apple", she is asking for.

Similarly any inversre trigonometric functions behaves like a Many-one Function; which means,

For Example $\sin^ {-1}\left (\frac {2} {3}\right)$ can have many solutions, we need to fix one solutions which can be used as standerd value for the function.

• A standerd value (Angles) of any inverse trigonometric value lies between a fiexed range is known as principal value. 

For Ex; The value of $\sin^ {-1}\left (\frac {2} {3}\right)$ will always lie between –? /2 to? /2.

$y={\sin }^{?1}\left(\frac{2}{3}\right)?\sin \left(y\right)=\frac{2}{3}?y?[?\frac{?}{2},\frac{?}{2}]$  

As per the NCERT Textbooks

“An integrated Chip consists of many passive and active components fabricated on a single chip of silicon. these ICs are compact, low-cost, and highly reliable. They consume less power and have high speed.”

These ICs are used in majority of our daily use electronics and all advance electronics. 

 A p-type semiconductor is electrically neutral despite having more holes, because the number of positively charged holes is exactly balanced/equal by the number of negatively charged acceptor ions introduced during doping. so practically untill any volatage is applied the semiconductor remains chargeless in other words doesn't produce any current even after doping.

 As per the NCERT Textbooks information"Although the number of holes is more than the number of electrons in a p-type semiconductor, the material as a whole is electrically neutral because the charge of holes is balanced by the negatively charged acceptor ions.”

As per NCERT Textbboks"If forward current is too large, it can produce large heating and damage the junction. So, a resistor is used in series with the diode to limit the current in the circuit.”

It means when a semiconductor diode is connected to a source under high current it causes excess heat due to more electrical energy. This excess heat is responsible to damage the junction in semiconductor diode permanently. Student can check out NCERT Solutions for Semicondutor Electronics of class 12 physics.  

The principle of mass-energy equivalence, given by Einstein's equation:

$E = mc^2$It states that mass and energy are interchangeable.

A small amount of mass can be converted into a large amount of energy because the speed of light $(c = 3 \times 10^8 \, \text {m/s})$ is very large and appears squared in the equation.

Significance in Nuclear Reactions:

• Helps in calculating the energy release in Nuclear Reactions
• Provides explanation for powering Nuclear Reactors and the Sun
• Explanation of Binding Energy of Nucleous

Nuclear Binding Energy is the amount of energy required to completely dismantle a nucleus into its individual protons and neutrons which is equivalent to the amount of energy to form a nucleous from its constituent nucleons (protons and neutrons).

Binding energy is calculated using Einstein's mass-energy equivalence relation:

$B.E. = \Delta m \cdot c^2$Where:

• $\Delta m$ = mass defect (in kg or amu)

• $c$ = speed of light $(3 \times 10^8 \, \text {m/s})$ (3*108m/s)