In solids: v = sqrt(Y/ρ) where v is the speed of sound, Y is the Young’s modulus, and ρ is the density of the material.

In gases: v = sqrt(γRT/M) where v is the speed of sound, γ is the adiabatic index, R is the universal gas constant, T is the temperature, and M is the molar mass of the gas.

If the electric lines of force intersected, there would be two directions for the electric field at the point of intersection, which would be contradictory. Hence, the lines of force never intersect.

To convert a moving coil galvanometer into an ammeter, a shunt resistor is connected in parallel with the galvanometer. This allows most of the current to pass through the shunt, while only a fraction passes through the galvanometer.

The torque τ on the coil is given by: τ = nIA B sin θ, where:

• n = 20 turns
• I = 0.5 A
• A = 800 mm² = 800 × 10⁻⁶ m²
• B = 0.3 T
• θ = 90°

Substituting the values:

τ = 20 × 0.5 × 800 × 10⁻⁶ × 0.3 × sin(90°) = 0.24 N m

Household appliances are connected in parallel to ensure that each appliance receives the same voltage and operates independently. This way, if one appliance fails, the others continue to function.

Faraday’s law states that the induced electromotive force (emf) in a closed loop is directly proportional to the rate of change of magnetic flux through the loop:

ε = - dΦ_B / dt

where ε is the induced emf and Φ_B is the magnetic flux.

The Q value is the difference in mass before and after the reaction, multiplied by c²:

Q = [m(Li) + m(H) - (m(He) + m(Q))]c²

Substitute the given masses:

Q = [7.016 + 1.008 - 4.008] = 4.016 u

Multiply by 931.5 MeV/c² to convert to energy:

Q = 4.016 × 931.5 MeV = 3.74 MeV

p-n-p transistor:

– The emitter is on the left with an arrow pointing outwards.

– The collector is on the right.

– The base is in the center.

n-p-n transistor:

– The emitter is on the left with an arrow pointing inwards.

– The collector is on the right.

– The base is in the center.

Modulation is the process of varying a carrier signal to transmit information (such as audio or video signals) over long distances. It is necessary to ensure the signal can travel efficiently over the medium (e.g., radio waves) and reduce interference.

– Pure resistor: The phase difference is 0° (current and emf are in phase).

– Pure inductor: The phase difference is +90° (current lags the emf by 90°).

– Pure capacitor: The phase difference is -90° (current leads the emf by 90°).

The critical angle is the angle of incidence above which total internal reflection occurs. Total internal reflection happens when light is traveling from a denser medium to a rarer medium, and the angle of incidence exceeds the critical angle.

The intensity of transmitted light varies as the square of the cosine of the angle between the transmission axis of the polarizer and the analyzer. The intensity will be maximum when the polaroids are aligned, and zero when they are crossed.

The magnetic field induction at a point on the equatorial line of a bar magnet is given by the expression:

B = (μ₀ / 4π) × (2M / r³)

where:

• μ₀ is the permeability of free space
• M is the magnetic moment of the magnet
• r is the distance from the center of the magnet

When capacitors are connected in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances:

1/C_eq = 1/C₁ + 1/C₂ + ...

Thus, the equivalent capacitance is:

C_eq = 1 / (1/C₁ + 1/C₂ + ...)

Kirchhoff’s law consists of two parts:

• Kirchhoff’s Current Law (KCL): The total current entering a junction is equal to the total current leaving the junction.
• Kirchhoff’s Voltage Law (KVL): The sum of the potential differences (voltage) around any closed loop in a circuit is zero.

For a Wheatstone bridge to be balanced, the following condition must hold:

(R₁/R₂) = (R₃/R₄)

Where R₁, R₂, R₃, and R₄ are the resistances of the four arms of the bridge.

De Broglie explained that particles such as electrons exhibit both particle and wave-like properties. His hypothesis was used to derive Bohr’s second postulate, which states that the angular momentum of an electron in an orbit is quantized:

mvr = nλ / 2π

Where n is the quantum number and λ is the de Broglie wavelength of the electron.

The neutron was discovered by James Chadwick in 1932. It was identified as a neutral particle with a mass approximately equal to that of the proton. The discovery of the neutron explained the missing mass in atomic nuclei and played a crucial role in the development of nuclear physics.

A semiconductor diode allows current to flow in only one direction. In a half-wave rectifier circuit, during the positive half-cycle of the input AC signal, the diode conducts and allows current to pass. During the negative half-cycle, the diode is reverse biased and does not conduct, resulting in a pulsating DC output.

Stationary waves in a stretched string are formed when two waves of the same frequency and amplitude travel in opposite directions. The point where the two waves meet and reinforce each other is called a node, and the points where they cancel out are called anti-nodes. The laws of transverse waves in a string are:

• The frequency of the wave depends on the tension and the linear mass density of the string.
• The velocity of the wave depends on the tension in the string and its mass per unit length.

The speed of transverse waves on the wire can be calculated using the formula:

v = sqrt(T/μ)

Where:

• T = 100 N (tension)
• μ = m/L = (6 x 10⁻³)/(0.6) = 10⁻² kg/m (mass per unit length)

Substituting the values:

v = sqrt(100 / 10⁻²) = 100 m/s

A moving coil galvanometer consists of a coil of wire suspended in a magnetic field. When current flows through the coil, it experiences a torque due to the magnetic field, causing the coil to rotate. The amount of rotation (deflection) is proportional to the current. The relation between the current I and the deflection angle θ is given by:

θ = kI

Where k is the constant of proportionality (a characteristic of the galvanometer).

To convert the galvanometer into a voltmeter, a series resistor is connected. The total resistance R_total should be such that the maximum current is 0.015A for a voltage of 1.5V. Using Ohm’s law:

V = I × R_total

Substituting the values:

1.5 = 0.015 × R_total

R_total = 1.5 / 0.015 = 100Ω

The series resistance required is:

R_series = R_total - R_galvanometer = 100Ω - 5Ω = 95Ω

A nuclear reactor operates based on the principle of nuclear fission. Uranium or plutonium atoms undergo fission when bombarded by neutrons, releasing energy in the form of heat. The heat is used to produce steam, which drives turbines to generate electricity. A reactor consists of the following components:

• Fuel rods – contain fissile material like uranium-235.
• Control rods – made of materials like boron, which absorb neutrons and control the fission rate.
• Moderator – slows down the neutrons to increase the probability of fission.
• Coolant – removes the heat produced during fission.