Curves a and b have different intensities but the same stopping potential, so curves 'a' and 'b' have the same frequency but different intensities.

Metal A
Since work function W = hv_o
and v_o > V_o so work function of metal A is more.
Aliter :
On stopping potential axis \(-\frac { { W }_{ o }^{ ' } }{ e } >-\frac { { W }_{ o } }{ e } \)
Hence work function W'o of metal A is more.

Laws of photoelectric effect:
(i) For a given surface, the emission of photoelectrons takes place only if the frequency of incident light is greater than a certain minimum frequency called the threshold frequency.
(ii) For a given frequency of incident light, the number of photoelectrons emitted is directly proportional to the intensity of the incident light. The saturation current is also directly proportional to the intensity of incident light.
(iii) Maximum kinetic energy of the photoelectrons is independent of the intensity of the incident light.
(iv) Maximum kinetic energy of the photoelectrons from a given metal is directly proportional to the frequency of incident light.
(v) There is no time lag between the incidence of light and the ejection of photoelectrons.

There are two ways of preparing the nanomateials, top down and bottom up approaches

The maximum range of propagation in this mode depends on
(i) transmitted power and
(ii) frequency (less than a few MHz) of high frequencies the rate of energy dissipation of the signal increases and the signal gets attenuated over a short distance.

(i) Because the transmission of signal directly from the transmitting antenna to receiving antenna called a line of sight communication.
(ii) The waves traveling directly from the transmitting antenna to the receiving antenna get blocked due to curvature of the earth.
(iii) It limits both the maximum line of sight distance between the two antennas arid also the maximum distance up to which transmission can be received.

i) FM requires a much wider channel.
ii) FM transmitters and receivers are more complex and costly.
iii) In FM reception, less area is covered compared to AM.

(i)  It is the branch of physics incorporated with technology towards the design of circuits using transistors and microchips.
(ii) It depicts the behavior and movement of electrons in a semiconductor, vacuum, or gas.
(iii) Electronics deals with electrical circuits that involve active components such as transistors, diodes, integrated circuits, and sensors, associated with the passive components like resistors, inductors, capacitors, and transformers.

(i) Fusion requires high temperature controlled reaction is not yet obtained. Highly sophisticated technology will be required.
(ii) However, the fuel is easily available, cheap and causes very less pollution.
(iii) There is no problem of waste management.
(iv) Fission controlled chain reaction is possible. The technology is well developed and established.
(v) There also exists the problem of waste management.

Atomic mass unit is defined as \(\frac{1}{12}\) ^th of the mass of one \(_{ 6 }^{ 12 }{ C }\) atom.
E = mc²
= 1.66 x 10-27 x 3 X 108 x 3 x 108 J
= 1.66 x 9 x 10-11 J
= \(\frac { 1.66\times 9\times { 10 }^{ -11 } }{ 1.6\times { 10 }^{ -13 } } \) MeV = 931 MeV.

The radius of the nth orbit 
\({ r }_{ n }=\frac { { n }^{ 2 }{ h }^{ 2 }{ \epsilon }_{ 0 } }{ \pi m{ Ze }^{ 2 } } \)
r₁ = 0.53Å
∴ The diameter of H₂ = 2 x r₁
= 0.53 x 2 = 1.06Å

During charging, the electric flux between the plates capacitor keeps on changing. This results in the production of displacement current between the plates.
\({ I }_{ d }=\varepsilon _{ 0 }\left( \frac { d{ \phi }_{ E } }{ dt } \right) \)

It provides electrical energy to satellites by means of solar cells. It is used to produce dehydrated fruits, in green houses to keep the plants warm, heat therapy for muscular pain or sprain, TV remote as a signal carrier, to look through haze fog or mist and used in night vision or infrared photography.

The required resistance has the least value for ammeter and maximum value in the case of a voltmeter.
(i) The shunt resistance required to convert a galvanometer to an ammeter has the value
S = \(\frac { { I }_{ g } }{ I-{ I }_{ g } } \) x G
The shunt required for the milliammeter be a higher value.
(ii) Similarly, The voltmeter should have high resistance, the value of the required resistance should be highest in the case of the voltmeter. This is connected in series with the coil of the galvanometer.

If the magnetic force \(\vec { F } =q(\vec { v } \times \vec { B } )\)
(i) The force on a charged particles is perpendicular to both \(\vec { v } \) and magnetic field \(\vec { B } \).
(ii) No, This is since the charged particle moves on a circular path.
\(\vec { F } =q(\vec { v } \times \vec { B } )\)
The particle does not gain energy.

(i) Magnetic field lines are continuous closed curves. The direction of magnetic field lines is from the North pole to the South pole outside the magnet and South pole to the North pole inside the magnet.
(ii) The direction of a magnetic field at any point on the curve is known by drawing a tangent to the magnetic line of force at that point.
(iii) Magnetic field lines never intersect each other.
(iv) The degree of closeness of the field lines determines the relative strength of the magnetic field. The magnetic field is strong where magnetic field lines crowd and weak where magnetic field lines thin out.

(i) Magnets are classified into natural magnets and artificial magnets.
(ii) For example, iron, cobalt, nickel, etc. are natural magnets.
(iii) Strengths of natural magnets are very weak and the shapes of the magnet are irregular.
(iv) Artificial magnets are made by us in order to have desired shape and strength.
(v) If the magnet is in the form of rectangular shape or cylindrical shape, then it is known as bar magnet.

(i) The total resistance offered to the flow of current due to resistance R, inductive resistance X_L, and capacitive reactance X_c in a circuit is called impedance.
It is given by \(z=\sqrt { { R }^{ 2 }+({ { X }_{ L }-{ X }_{ C }) }^{ 2 } } \)
(ii) At resonance, when X_L= X_C

(i) The electromagnetic oscillations of LC system can be compared with the mechanical oscillations of a spring-mass system.
(ii) There are two forms of energy involved in LC oscillations. One is electrical energy of the charged capacitor; the other magnetic energy of the inductor carrying current.
(iii) Likewise, the mechanical energy of the spring-mass system exists in two forms; the potential energy of the compressed or extended spring and the kinetic energy of the mass. The Table lists these two pairs of energy.
(iv) By examining, the analogies between the various quantities can be understood and these correspondences.
(v) The angular frequency of oscillations of a spring-mass is given by equation
\(\omega =\sqrt { \frac { k }{ m } } \)
k ⟶ \(\frac { 1 }{ C } \) and m ⟶ L. Therefore, the angular frequency of LC oscillations is given by
ω = \(\frac { 1 }{ \sqrt { LC } } \)

(i) Suppose n cells, each of emf \(\xi \) volts and internal resistance r ohms are connected in series with an external resistance R.
(ii) The total emf of the battery = \(n\xi \) The total resistance in the circuit = nr + R By Ohm's law, the current in the circuit is 
\(I=\cfrac { totalemf }{ taoal\ resistance } =\cfrac { n\xi }{ nr+R } \)
\(I=\cfrac { n\xi }{ R } =n{ l }_{ 1 }\)
(iii) where II is the current due to a single cell
\(\left( { I }_{ 1 }=\cfrac { \xi }{ R } \right) \)
Thus, if r is negligible when compared to R the current supplied by the battery is n times that supplied by a single cell.
Case (b) If r >> R,\(I=\cfrac { n\xi }{ nr } =\cfrac { \xi }{ r } \)
(iv) It is the current due to a single cell. That is, current due to the whole battery is the same as that due to a single cell and hence there is no advantage in connecting several cells.
(v) Thus series connection of cells is advantageous only when the effective internal resistance of the cells is negligibly small compared with R.

(a) An electric cell converts chemical energy into electrical energy to produce electricity. It contains two electrodes immersed in an electrolyte as shown Several electric cells connected together form a battery.

(b) When a cell or battery is connected to a circuit, electrons flow from the negative terminal to the positive terminal through the circuit. By using chemical reactions, a battery produces potential differences across its terminals. This potential difference provides the energy to move the electrons through the circuit.

(i) A dielectric is a non-conducting material and has no free electrons. The electrons in a dielectric are bound within the atoms. Ebonite, glass and mica are some examples of dielectrics.
(ii) When an external electric field is applied, the electrons are not free to move anywhere but they are realigned in a specific way. A dielectric is made up of either polar molecules or non-polar molecules.

(i) Suppose the electric field is not uniform and the area A is not flat (Figure), then the entire area is divided into n small area segments \(\Delta { \overset { \rightarrow }{ A } }_{ 1 },\Delta { \overset { \rightarrow }{ A } }_{ 2 },\Delta { \overset { \rightarrow }{ A } }_{ 3 }.....\Delta { \overset { \rightarrow }{ A } }_{ n },\) such that each area element is almost flat and the electric field through each area element is considered to be uniform.
(ii) The electric flux for the entire area A is approximately written as
\({ \Phi }_{ E }={ \overset { \rightarrow }{ E } }_{ 1 }.\Delta { \overset { \rightarrow }{ A } }_{ 1 },{ \overset { \rightarrow }{ E } }_{ 2 }.\Delta { \overset { \rightarrow }{ A } }_{ 2 },{ \overset { \rightarrow }{ E } }_{ 3 }.\Delta { \overset { \rightarrow }{ A } }_{ 3 }.....{ \overset { \rightarrow }{ E } }_{ n }.\Delta { \overset { \rightarrow }{ A } }_{ n },\)
\(\sum _{ i=1 }^{ n }{ { \overset { \rightarrow }{ E } }_{ 1 }.\Delta { \overset { \rightarrow }{ A } }_{ 1 } } \quad \quad \quad ....(1)\)

(iii) By taking the limit \({ \overset { \rightarrow }{ A } }_{ 1 }\rightarrow 0\) (for all i) the summation in equation (1) becomes integration. The total electric flux for the entire area is given by
\({ \Phi }_{ E }=\int { { \overset { \rightarrow }{ E } } } .d\overset { \rightarrow }{ A } \quad\quad ....(2)\)
(iv) From Equation (2), it is clear that the electric flux for a given surface depends on both the electric field pattern on the surface area and orientation of the surface with respect to the electric field.

(i) The potential energy difference per unit charge is given by
\(\frac { \Delta U }{ q' } =\frac { q'\int _{ R }^{ P }{ (-\overset { \rightarrow }{ E } ) } .d\overset { \rightarrow }{ r } }{ q' } =\int _{ R }^{ P }{ \overset { \rightarrow }{ E } } .d\overset { \rightarrow }{ r } \quad ...(1)\)
(ii) The above equation (1) is independent of q'. The quantity \(\frac { \Delta U }{ q' } =\int _{ R }^{ P }{ \overset { \rightarrow }{ E } } .d\overset { \rightarrow }{ r } \) is called electric potential difference between P and R and is denoted as V_P - V_R = ∆V.
(iii) In other words the electric potential difference is also defined as the work done by an external force to bring unit positive charge from point R to point P.
\({ V }_{ p }-{ V }_{ R }=\Delta V=\int _{ R }^{ P }{ \overset { \rightarrow }{ E } } .d\overset { \rightarrow }{ r } \)
(iv) The electric potential energy difference can be written as ∆U = q' ∆V.