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Power = I\(^2\)R = \((\frac{E}{R + r})^2 R\) To get point of maximum power transfer, we take the derivative and equate it to 0. \(P = E^2 (\frac{R}{(R + r)^2})\) \(\frac{\mathrm d P}{\mathrm R} = E^2 (\frac{(R + r)^2 - 2R(R + r)}{(R + r)^4})\) = \(E^2 (\frac{(R + r)[(R + r) - 2R}{(R + r)^4})\) \(\frac{\mathrm d P}{\mathrm d R} = E^2 (\frac{r - R}{(R + r)^3})\) Maximum power is gotten when r - R = 0 i.e. r = R.

The r.m.s value of an a.c voltage/current is the value of the d.c. voltage/ current that will dissipate the same amount of energy in a given resistance as the a.c. Thus the r.m.s value of the a.c supply is 12v.

Generally, the viscosity of liquids tends to increase with pressure, as the increased pressure can lead to a greater interaction between molecules

Energy density = \(\frac{\text{Energy}}{\text{Volume}}\) = \(\frac{\text{Joule}}{m^3}\) = \(\frac{kg m^2 s^{-2}}{m^3}\) = kgm\(^{-1}\)s\(^{-2}\)

I. Work done by load is always less than the work done by effort. This statement is generally true for all machines because some of the work done by the effort is used to overcome friction and other resistive forces in the machine. III. A fishing rod is a machine. This statement is true as a fishing rod is a simple machine that uses a lever to catch fish.

E = hf f = (E)/h ∴ f = (3.3 x 1.6 x 10-19)/6.6 x 10-34 = 0.8 x 1015 = 8.0 x 1014 Hz

This process occurs when the thermal energy of the metal is sufficient to allow electrons to overcome the work function and escape from the surface.

Band Theory: This theory describes the energy levels of electrons in solids as bands. It explains how the bands (valence and conduction bands) determine the electrical properties of materials.

I. The number of neutrons released exceeds the number that caused the fission. fission releases additional neutrons that can initiate further reactions. II. There is loss of mass. mass is converted into energy according to Einstein’s equation E = mc\(^2\) III. Energy is produced. significant energy is released during the fission process.

Rectification: A diode allows current to flow in one direction, making it suitable for converting alternating current (AC) to direct current (DC). Diodes are commonly used in power supplies to rectify AC voltage.

Pressure of the Gas, P = A + h = 76 + 10 86 cm Hg

IF the volume of gas is plotted against the reciprocal of pressure, the slope will be given as Slope = V/1/P = P x V thus the unit of the slope will be; P = ForceArea = Nm-2, = V = M3 = NM. The unit NM (Newton - Meter) is the practical unit of work, which is the product of force (N) and Displacement (M). Note: It should be noted that the practical unit of work is Newton-Meter, whereas its S.I unit is Joules, just as energy.

Power = force x velocity => 80,000 = F x 32 F = \(\frac{80000}{32}\) = 2500N = 2.50 x \(10^3\)N

No expanded working has been attached for this question yet. The verified answer is Option B.

Volume immersed solid = 3 x 105 x \(\frac{2}{3}\) = 2 x 105m3 Mass of liquid displaced = ev = 2 x 105 x 900 = 18 x 107 kg Upthrust = 18 x 107 x 10 = 7.8 x 109N Mass of solid = ev = 2.5 x 103 x 105 = 7.5 x 108 Weight of solid = 7.5 x 108 x10 = 7.8 x 109 Reading = 0.75 - 0.18 = 0.57N