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CONCEPT:

• For a charged Spherical conducting shell, the Electric field inside the shell is zero.
• The electric field at point P distance r from the center of charged conducting shell (at a point outside the shell)  of radius R having charge q is given as

\(E = \frac{q}{4\pi \epsilon _0 r^2}\)

• Overall the Electric Field due to charged conducting shell is given as

E = 0, ( r < R )

\(E = \frac{q}{4\pi \epsilon _0 R^2}\) ( r = R)

\(E = \frac{q}{4\pi \epsilon _0 r^2}\) (r > R)

where r is the distance of the point from the center of the shell, and R is the radius of the Shell.

EXPLANATION:

• It has been asked to find the electric field at a distance R /2 from the center, Clearly, the point R /2 from the center lies inside the shell.

• Electric Field inside the shell is zero. So, the electric field at distance R/2 will be zero.

• Aspirants may make mistakes by considering the distance R/2  from the outer of shell.

Additional Information

• The expression for the electric field due to charged spherical conducting shell has been obtained from Gauss Law.
• The expression will remain the same for insulating charged spherical shell and solid conducting sphere.

CONCEPT:

There are mainly two ways of combining resistances:

1. Resistances in series combination
2. Resistances in parallel combination

• When two or more resistances are connected one after another such that the same current flows through them- this system is called series combination

The net resistance/equivalent resistance (R) of resistances in series is given by:

Equivalent resistance, R = R1 + R2

• When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called as resistances in parallel.

The net resistance/equivalent resistance(R) of resistances in parallel is given by:

\(\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}\)

Calculation:

The 10Ω and 0Ω resistors are in parallel:

⇒ 1/Rparallel = 1/10 + 1/0

⇒ Since 1/0 is undefined, the parallel combination results in 0Ω for practical purposes.

⇒ The total resistance in the circuit is the sum of the series of resistances:

⇒ Rtotal = 5Ω + 0Ω + 5Ω

⇒ Rtotal = 10Ω

⇒ Using Ohm's Law to find the current:

⇒ I = V / Rtotal

⇒ I = 10V / 10Ω

⇒ I = 1A

∴ The current in the given electric circuit is 1A.

EXPLANATION:

Rectifier:

• A rectifier is a device which converts an alternating current into a direct current. A p-n junction can be used as a rectifier because it permits current in one direction only.

Amplification:

• A device which increases the amplitude of the input signal is called amplifier. An n-p-n or p-n-p transistor is used as a transistor to increase the amplitude of the input signal.

Modulation:

• Modulation is the process by which some characteristic, usually amplitude, frequency or phase angle of a high frequency carrier wave is varied in accordance with the instantaneous value of the low frequency audio signal called the modulating signal.

Filtration:

• Filtration or a filter circuit is a device to remove the A.C components of the rectified output, but allows the D.C components to reach the load. A filter circuit is in general a combination of inductor (L) and Capacitor (C) called LC filter circuit.
• Out of all these only rectifier is a device which uses diode.

correct answer is Rectifier

Key Points

Rectifier: It is an electrical device that converts alternating current (AC), to direct current (DC). 

Rectifiers are widely used in electronics systems because most of our equipment runs on direct current (DC), but the supply we get into our households is alternating current.

Diode: It is a two-terminal electronic component that allows current to flow in a single direction. 

Half wave rectifier.

Full-wave rectifier.

Center tap full-wave rectifier.

Concept:

The radius of the circular path of a charged particle moving perpendicular to a uniform magnetic field is given by:

r = mv / (qB)

Here, m is the mass, v is the speed, q is the charge, and B is the magnetic field strength.

The ratio of radii for a proton and an alpha particle is:

r_p / r_α = (m_pv_p/q_p) ÷ (m_αv_α/q_α)

Both particles have the same kinetic energy:

K = (1/2)mv² ⇒ v = √(2K/m)

Substituting v into the ratio:

r_p / r_α = (m_p/q_p)√(1/m_p) ÷ (m_α/q_α)√(1/m_α)

Using m_α = 4m_p and q_α = 2q_p:

r_p / r_α = [(1/4) × (2/1)] × √(4) = 1

Final Answer: The radii of the proton and alpha particle trajectories are equal (ratio = 1).

CONCEPT:

• A Transformer is used to convert low voltage (or high current) to high voltage (or low current) and high voltage to low voltage.

• It works on the principle of electromagnetic induction.

• The primary coil has Np turns. The other coil, called a secondary coil, has Ns turns.

• Generally, the primary coil works as the input coil, and the secondary coil works as the output coil of the transformer.

• When an AC voltage is applied to the primary coil, the resulting current produces an alternating magnetic flux that links the secondary coil and induces an emf in it. The value of this emf depends on the number of turns in the secondary.

• In a transformer, the voltage in secondary is calculated by

​\(\frac{N_{s}}{N_{p}}=\frac{V_{s}}{V_{p}}\)

Here, Np and Ns are the numbers of turns in the primary and the secondary coils respectively and Vp and Vs are the rms voltages across the primary and secondary respectively.

• In the transformer, the load is connected to the secondary coil while the primary coil of a transformer is connected to an AC source.

CALCULATION: 

Given - η = 80%, V_s = 440 V, I_s = 2A, and V_P = 220V

• The output and input power of the transformer is given by

Input Power (P_I) = V_P × I_P = 220 × I_P 

Output power (P_o) = V_s × I_s= 440 × 2 = 880 W

• The efficiency (η) of the transformer is given by

\(\Rightarrow \eta=\frac{Output, power}{Input, power}\)

\(\Rightarrow \eta=\frac{P_0}{P_i} \)

\(\Rightarrow 80=\frac{880}{220\times I_p}\times 100\)

\(\Rightarrow I_{P} =5A\)

CONCEPT:

• A choke coil is a low resistance inductor coil used to suppress or limit the flow of alternating current without affecting the flow of direct current, as in applications that require conversions of AC to DC.

• Thus a choke can be represented by a series RL circuit.

• In a tube light, a choke is an inductor that is used to induce a high voltage across the tube light.

• Then gas inside the starter gets ionized due to this full voltage and heats the bimetallic strips that are caused to bent to connect to the fixed contact.

• The power consumed by a choke coil is given by

P = V I Cosϕ

Where V = Voltage, I = Current, Φ = Phase angle

EXPLANATION :

• The average power consumed by an inductor is given by

⇒ P_av =  I²_rms R

Since the Resistance is negligible then P_av can be written as

⇒ P_av = 0 

• Hence, option 1 is the answer

Concept:

Refraction of Light –

• The bending of the ray of light passing from one medium to the other medium is called the refraction of light.
• The refraction of light takes place on going from one medium to another because the speed of light is different in the two media.
• When a ray of light goes from a rarer medium to a denser medium, it bends towards the normal.
• When a ray of light goes from a denser medium to a rarer medium, it bends away from the normal.

Explanation:

• The refraction of light through the atmosphere is responsible for many interesting phenomena. For example, the Sun is visible a little before the actual sunrise and until a little after the actual sunset due to refraction of light through the atmosphere.
• The layers of air nearer to earth are denser than those above it.
• At sunrise and sunset when the sun is below the horizon, the light rays starting from the sun are incident on these layers.
• They pass through successively denser layers and thus get bent more and more towards the normal until they fall upon the eye of the observer.
• To the observer, these rays appear to come from S’ which is above the horizon. It is for this reason that the sun is visible to us a little before it rises above the horizon and so also till a little later it sets below the horizon.
• The difference of time is about 2 minutes each for an early rise and late setting of the Sun.

Concept:

Power of Lenses in Combination:

• The power of a lens is the reciprocal of its focal length:
• P = 1 / f (where P is the power in diopters (D) and f is the focal length in meters)
• When two lenses are in contact, the total power of the combination is the sum of the individual powers:
• P_total = P₁ + P₂
• Where P₁ and P₂ are the powers of the individual lenses.
• The focal length of the combination can be found using: f_total = 1 / P_total

Calculation:

Given,

Power of the first lens, P₁ = -15D

Power of the second lens, P₂ = +5D

Total power of the combination,

P_total = P₁ + P₂

P_total = -15D + 5D = -10D

Now, the focal length of the combination is given by:

f_total = 1 / P_total

f_total = 1 / (-10) = -0.1 m

∴ The focal length of the combination is -10 cm. Hence, the correct option is 2) -10 cm.

• Polarization refers to the direction of the electric field in an electromagnetic wave.
• A wave whose electric field is oscillating in the vertical direction is said to be polarized in the vertical direction.
• The photons of such a wave would interact with matter differently than the photons of a wave polarized in the horizontal direction.
• The electric field in light waves from the sum vibrates in all directions, so direct sunlight is unpolarized.
• Sunlight reflected from a surface is partially polarized, parallel to the surface.
• Radio waves, x-rays, and light waves can be polarized, but the acoustic wave cannot be polarized because it can not propagate through a vacuum.