Fringe width \(\beta =\cfrac { D\lambda }{ d } \Rightarrow \beta =\lambda \) for same D and d. When the whole apparatus is immersed in a transparent liquid of refractive index n = 4/3, the wavelength decreases to \({ \lambda }^{ ' }=\cfrac { \lambda }{ n } =\cfrac { \lambda }{ 4/3 } \) width decreases to \(\cfrac { 3 }{ 4 } \) times.

(i) When lens is immersed in water, it behaves as a convex lens but its focal length will increase.
(ii) When convex lens is immersed in carbon - disulphide, it will behave as a concave lens.

(i) Light must travel from denser to rarer medium,
(ii) Angle of incidence in the denser medium must be greater than critical angle (i > i_c).

The stopping potential does not depend on the intensity of incident radiation; so stopping potential will remain unchanged.

Nano science is the science of objects with typical sizes of 1-100 nm. Nano means One - billionth of a meter that is 10^-9 m.

It is a combination of receiver and transistor placed along the path of signal so as to extend the range of the communication system.

Electric field is strong enough to break (or) rep tune the covalent bonds in the lattice and there by generating electron - hole pairs. This effect is called Zener effect.

The energy band formed due to the valence orbitals is called valance band and that formed due to unoccupied orbital is called conduction band.

In nuclear fusion reaction, the energy liberated per unit mass of the nuclei taking part in the reaction is many times larger than the energy liberated in a fission reaction.

(i) Speed of Electromagnetic wave \(=\frac{Peak\ value\ of\ Electric\ field}{Peak\ value\ of\ magnetic\ field}\)
\(c=\frac { { E }_{ 0 } }{ { B }_{ 0 } } \)
(ii) Yes, As Electromagnetic waves contain both electric and magnetic fields, there is a non-zero energy density associated with it.
\(E=\frac { hc }{ \lambda } \)
Momentum p \(=\frac{Total\ energy\ transferred\ to\ the\ surface}{Velocity\ of\ light\ in\ vacuum}\)
i.e.p = \(\frac{U}{c}=mc\)
U - total energy transferred to the surface.
EM waves carry not only energy and momentum but also angular momentum.

Energy stored in the capacitor \(\frac{1}{2}CV^2=\frac{q^2}{{2C}}\)

Net capacitance of the parallel combination (when capacitors are connected to getter)
= C + C = 2C
Since the total charge Q remains same initial energy.
\({ U }_{ 1 }=\frac { { q }^{ 2 } }{ 2C } \)
Final energy \({ u }_{ f }=\frac { { q }^{ 2 } }{ 2(2C) } \)
\(\frac { { U }_{ f } }{ { U }_{ i } } =1:2\)

The given graph represents E ∝ \(\frac{1}{C}\)
This is satisfied by the expression E = \(\frac{q^2}{2c}\)
E ∝ \(\frac{1}{C}\)
i.e. the charge q is kept constant.

If we hold the current carrying conductor in our right hand such that the thumb points in the direction of current flow, then the fingers encircling the wire points in the direction of the magnetic field lines produced.

(i)  γ =  γ_r occurs when X_L = X_C. Then the circuit becomes purely resistive. So current and voltage will be in the same phase.
(ii) X_L = 2π γL and \({ X }_{ c }=\frac { 1 }{ 2\pi \gamma c } \)
When γ =  γ_r, XL is small and Xc is large the circuit is capacitive, so current leads the voltage in phase.
The circuit is inductive. So current lags behind the voltage in phase.

\(I=\cfrac { E }{ R+r } \)

At the transmitting point, the voltage is increased and the corresponding current is decreased by using a step-up transformer. Then it is transmitted through transmission lines. This reduced current at high voltage reaches the destination without any appreciable loss. At the receiving point, the voltage is decreased and the current is increased to appropriate values by using a step-down transformer, and then it is given to consumers.

\({ V }_{ d }=\cfrac { eE }{ m } \tau =\cfrac { eV }{ ml } .\tau \left[ E=\cfrac { V }{ l } \right] \)
Keeping V constant, if 1 is doubled, v_d is halved. Again keeping area constant if length is doubled, if R will be doubled [R \(\alpha\) 1,if a is constant].

When current flows through a resistor, some of the electrical energy delivered to the resistor is converted into heat energy and it is dissipated. This heating effect of current is known as Joule's heating effect.

The total energy used by any device is obtained by multiplying the power and duration of the time when it is ON. Unit of the energy will be in joules. (or) watt second. Electrical energy is measured in kilowatt hour (kWh). 1 kWh is known as 1 unit of electrical energy. (1 kWh = 1000 Wh = (1000 W) (3600 s), 1 kWh = 3.6 x 10⁶ J)

The electrical power P is the rate at which the electrical potential energy is delivered
\(P=\cfrac { dW }{ dt } =\cfrac { d }{ dt } \left( V.dQ \right) =V\cfrac { dQ }{ dt } \)
Since the electric current \(I=\cfrac { dQ }{ dt } \).
So the equation (1) can be rewritten as P = VI
This expression gives the power delivered by the battery to any electrical system, where I is the current passing through it and V is the potential difference across it. The SI unit of electrical power is a watt.

a) I ∝ \(\frac{1}{r^2}\)
b) V ∝ \(\frac{1}{r}\)
c) V does not depend on r.

Energy density U\(=\frac { 1 }{ 2 } { \varepsilon }_{ 0 }{ E }_{ 2 }\)
But \(E=\frac { \sigma }{ { \varepsilon }_{ 0 } } =\frac { Q }{ { A\varepsilon }_{ 0 } } \)
\(\therefore U=\frac { 1 }{ 2 } .\frac { { \varepsilon }_{ 0 }{ Q }_{ 2 } }{ { A }^{ 2 }{ \varepsilon }_{ 0 } } \Rightarrow U=\frac { { Q }_{ 2 } }{ 2A^{ 2 } } \)
\(U\alpha \frac { 1 }{ { A }^{ 2 } } \Rightarrow { U }_{ A }>{ U }_{ B }\)

(i) In stable equilibrium the dipole moment is parallel to he direction of electric field. i.e. θ = 0.
 θ = 0^o \(\overset { \rightarrow }{ P } \) is parallel to stable \(\overset { \rightarrow }{ E } \) equilibrium
(ii) In unstable equilibrium, P.E. is max., so θ = π. i.e. dipole moment is antiparallel to electric field.
θ = 180°. \(\overset { \rightarrow }{ P } \) is antiparallel

Net electric flux is zero because
(i) It is independent to the shape and size
(ii) Net charge of the electric dipole is zero.

When an external electric field is applied, the centers of positive and negative charges are separated by a small distance which induces dipole moment in the direction of the external electric field. Then the dielectric is said to be polarized by an external electric field.