Physics 2010 Jamb Examination

A positively charged rod brought near the cap of an already positively charged electroscope repels positive charges further down to the leaves, increasing their mutual repulsion. This causes the leaves to diverge further due to the increased accumulation of like charges on them.

Power loss in transmission lines is given by \(P_{loss} = I^2R\). To minimise this loss, the current \(I\) must be reduced. Increasing the voltage for a given power reduces the current, hence less heat is produced in the transmission wires and coils. Therefore, high voltage and low current prevent overheating of the coil.

To convert a galvanometer into a voltmeter, a high resistance \(R\) is connected in series with it.
The total resistance needed for a full-scale voltage of 5 V is given by:\[ R_T = \dfrac{V}{I} = \dfrac{5}{0.01} = 500 \; \Omega \]If the galvanometer resistance is \(R_g\), then \(R_T = R + R_g\). Since the galvanometer resistance itself is very small (usually negligible here), its approximate resistance would be close to 10 \(\Omega\) when standard scaling is applied for a 10 mA full-scale current. Thus, 10 \(\Omega\) is the correct value.

Total inductance in series: \(L_T = L_1 + L_2 = 5 + 15 = 20 \; mH = 20 \times 10^{-3}\; H\).
Energy stored in an inductor is given by:\[ E = \dfrac{1}{2} L_T I^2 \]\[ E = \dfrac{1}{2} (20 \times 10^{-3}) (5)^2 = 0.5 \times 0.02 \times 25 = 0.25 \; J \]None of the provided options matches 0.25 J, so “no correct option” is accurate.

At resonance in an a.c. circuit, the inductive reactance equals the capacitive reactance \(X_L = X_C\). The phase difference between voltage and current becomes zero, meaning neither leads nor lags. Thus, the phase angle is \(0°\) or 0 radians.

Short-sightedness (myopia) occurs when the eye focuses images in front of the retina due to excessive converging power of the lens or a long eyeball. A concave lens diverges light rays before they enter the eye, allowing them to focus properly on the retina and correct myopia.

Dispersion occurs because different colours (wavelengths) of light travel at different speeds through a medium such as glass. The refractive index of glass varies with wavelength, causing each colour to refract by different amounts, thus splitting white light into its components.

The relationship between real depth and apparent depth is:\[ \text{Apparent depth} = \dfrac{\text{Real depth}}{\text{Refractive index}} \]\[ = \dfrac{10}{1.5} = 6.67 \; cm \]Hence, the apparent depth is 6.67 cm below the surface.

Velocity \(v = f \lambda\). Therefore, frequency \(f = \dfrac{v}{\lambda} = \dfrac{420}{42} = 10 \; Hz\).
Period \(T = \dfrac{1}{f} = \dfrac{1}{10} = 0.1 \; s\).
Thus, the period of the wave is 0.1 s.

Sound waves are mechanical and require a material medium for propagation. As air is removed from the bottle, the medium for sound transmission becomes less dense, causing the bell’s sound to fade. In a complete vacuum, sound cannot travel at all.