Physics 2012 Jamb Examination

Dispersion occurs because white light is made up of different wavelengths (colours), each refracted by a different amount when passing through a medium like a prism. Shorter wavelengths, such as violet, bend more than longer wavelengths, such as red, causing the light to spread into its component colours—forming a spectrum. This separation of colours by refraction defines the phenomenon of dispersion.

Although both the accumulator and the dry cells have the same e.m.f of 12V, the accumulator can deliver a much larger current due to its lower internal resistance and higher current capacity. Car starter motors require a large current to operate, which dry cells cannot supply without a significant voltage drop. Therefore, the inability of dry cells to provide sufficient current makes them unsuitable for starting cars.

A fuse must be connected to the live wire so that when an overcurrent occurs, it breaks the live circuit, disconnecting the device from the power source completely. If the fuse were connected to the neutral or earth wire, the circuit could remain live even when the fuse blows, posing a severe risk of electric shock. The live connection ensures that the entire circuit is safely isolated during a fault.

The force on a charged particle moving perpendicularly to a magnetic field is given by:\[F = Bqv\] Rearranging for \(B\):\[B = \dfrac{F}{qv}\] Substituting the values:\[B = \dfrac{1.8 \times 10^{-8}}{(1.0 \times 10^{-8})(3.0 \times 10^{2})}\]\[B = \dfrac{1.8 \times 10^{-8}}{3.0 \times 10^{-6}} = 6.0 \times 10^{-3} \; \text{T}\] Therefore, the magnetic field strength is \(6.0 \times 10^{-3} \; \text{T}\).

The root mean square (r.m.s.) or effective value of an alternating current is related to its maximum value by:\[I_{rms} = \dfrac{I_0}{\sqrt{2}}\]where \(I_0 = 10\,A\).\[I_{rms} = \dfrac{10}{1.414} = 7.07 \approx 7.1 \; \text{A}\]The r.m.s. value corresponds to the d.c. equivalent current that produces the same heating effect in a resistor as the alternating current. Hence, the d.c. equivalent is 7.1 A.

The induced e.m.f. in a conductor moving in a magnetic field is given by:\[E = B l v \sin \theta\]where \(B = 1.5\,\text{Wb/m}^2\), \(l = 1\,\text{m}\), \(v = 50\,\text{m/s}\), and \(\theta = 30^\circ\).\[E = 1.5 \times 1 \times 50 \times \sin 30^\circ\]\[E = 75 \times 0.5 = 37.5 \; \text{V}\]Thus, the induced e.m.f. is 37.5 V.

X-rays used for medical imaging are employed in diagnostic radiology. They enable the internal visualisation of the human body to locate foreign objects such as swallowed pins, fractures, or tumours. Therapeutic X-rays are used for treatment, while crystallography and mammography are specialised techniques for analysing crystals and breast tissues respectively. Hence, detecting a swallowed pin is an application of diagnostic X-rays.

Gamma rays are high-energy electromagnetic waves and have no charge or mass. As a result, they are unaffected by electric and magnetic fields. In contrast, alpha and beta particles are charged and are therefore deflected in such fields. Gamma rays continue to move in straight lines regardless of field presence, which is a defining property of uncharged radiation.

Each half-life reduces the number of undecayed atoms by half:
After 1 half-life (20 s): 500 atoms remain
After 2 half-lives (40 s): 250 atoms remain
After 3 half-lives (60 s): 125 atoms remain
Thus, it takes 3 half-lives, i.e., \(3 \times 20 = 60\) seconds, for the sample to decay from 1000 atoms to 125 atoms.

A p–n junction diode allows current to flow easily in the forward-biased condition (when the p-side is connected to the positive terminal) and blocks current in the reverse-biased condition. This unidirectional property enables it to convert alternating current (a.c.) into direct current (d.c.) by allowing current flow only during one half of the cycle, hence functioning as a rectifier.