Physics 2022 Jamb Examination

Electricity is conducted in liquids through the movement of ions. Tap water, sea water, and drinking water all contain dissolved salts and minerals that dissociate into ions, allowing current to flow. Distilled water, however, has had these impurities removed through the distillation process. Because it lacks significant ions to act as charge carriers, it is a very poor conductor of electricity.

We can determine the number of half-lives (\( n \)) by seeing how many times the initial activity must be halved to reach the final activity:\[ 120 \xrightarrow{1} 60 \xrightarrow{2} 30 \xrightarrow{3} 15 \]This shows that 3 half-lives have passed in 6 days. Alternatively, using the formula:\[ A = A_0 \left(\frac{1}{2}\right)^n \]\[ 15 = 120 \left(\frac{1}{2}\right)^n \]\[ \frac{15}{120} = \left(\frac{1}{2}\right)^n \]\[ \frac{1}{8} = \left(\frac{1}{2}\right)^n \Rightarrow n = 3 \]To find the half-life (\( T_{1/2} \)):\[ T_{1/2} = \frac{\text{Total time}}{n} = \frac{6}{3} = 2 \text{ days} \]

In the subtractive colour model (pigments and dyes), the primary colours are Cyan, Magenta, and Yellow (CMY). These are called secondary pigments when discussed in relation to the primary colours of light (Red, Green, and Blue). When you mix primary pigments, you subtract wavelengths from reflected light.

This phenomenon is a result of refraction, which is the bending of light as it passes from one medium (water) to another (air) of different optical density. As light travels from the water into the air to reach the observer's eye, it speeds up and bends away from the normal. This causes the submerged object to appear closer to the surface than it actually is, making the person's legs look shorter.

The velocity of a wave is the product of its frequency and its wavelength. This is represented by the wave equation:\[ v = f\lambda \]Given:\[ f = 312 \text{ Hz} \]\[ \lambda = 1.10 \text{ m} \]Substituting the values:\[ v = 312 \times 1.10 = 343.2 \text{ ms}^{-1} \]

The capacitance (\( C \)) of a parallel plate capacitor is determined by the physical characteristics of the plates and the dielectric between them. The formula is:\[ C = \frac{\varepsilon A}{d} \]Where \( A \) is the area of the plates and \( d \) is the distance between them. Since \( C \) is directly proportional to \( A \), increasing the plate area allows more charge to be stored for a given potential difference, thereby increasing the capacitance.

A magnetic relay is an electromagnetic switch. It uses a small current flowing through a coil to create a magnetic field, which then pulls a switch to open or close another circuit.

This allows a low-power circuit (like a microchip or a simple switch) to safely control a high-power circuit (like an industrial motor or car starter) that carries a much larger current.

The kinetic molecular theory of gases states that gas particles are in constant, random motion and are separated by distances that are very large compared to their own size. Because the intermolecular forces are negligible in this state, the molecules spread out to fill the entire volume of any container they are placed in.

Options A and B describe solids, while option D describes liquids.

The electrical energy (\( E \)) dissipated by a resistor is given by the product of voltage, current, and time:\[ E = IVt \]Given:\[ I = 0.5 \text{ A} \]\[ V = 40 \text{ V} \]\[ t = 2 \text{ minutes} = 2 \times 60 = 120 \text{ seconds} \]Calculation:\[ E = 0.5 \times 40 \times 120 \]\[ E = 20 \times 120 = 2400 \text{ J} \]

Surface charge density (the concentration of charge) on a conductor is not uniform unless the conductor is a perfect sphere. For an irregularly shaped conductor, the charge accumulates most densely at regions with the greatest curvature (the sharpest points). Looking at the pear shape, point X represents the sharpest end or the region with the highest curvature, so the charge concentration will be highest there.