Physics 2014 Jamb Examination

To reduce the total resistance of a circuit, a resistor must be added in parallel. The formula for total resistance \( R_T \) in parallel is: \[ \frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} \] Given \( R_1 = 200\Omega \) and the desired \( R_T = 120\Omega \): \[ \frac{1}{120} = \frac{1}{200} + \frac{1}{R_2} \] \[ \frac{1}{R_2} = \frac{1}{120} - \frac{1}{200} \] The LCM of 120 and 200 is 600: \[ \frac{1}{R_2} = \frac{5 - 3}{600} = \frac{2}{600} \] \[ R_2 = \frac{600}{2} = 300\Omega \] Thus, a 300Ω resistor must be connected in parallel.

PHCN (now DisCos in Nigeria) and other utility companies measure electrical energy consumption in kilowatt-hours (kWh). While the Joule (J) is the SI unit for energy, it is too small for commercial billing. One kilowatt-hour represents the energy consumed by a 1000-watt appliance running for one hour.

While hammering and heating can demagnetize a magnet, the most complete and efficient 'best' method is the electrical (solenoid) method. The magnet is placed inside a solenoid connected to an alternating current (AC) source. As the magnet is slowly withdrawn to a distance while the current is still flowing, the rapidly reversing magnetic field gradually reduces the alignment of the magnetic domains to zero.

The angle of dip (magnetic inclination) is the angle that the Earth's magnetic field lines make with the horizontal plane. At the magnetic equator, the magnetic field lines are perfectly horizontal, so the angle of dip is 0°. At the magnetic poles, the lines are vertical, resulting in an angle of dip of 90°.

In standard beta decay (\(\beta^-\)), a neutron in the nucleus transforms into a proton and an electron (the beta particle).

Since a neutron is replaced by a proton, the mass number stays the same, but the number of protons (atomic number) increases by one.

Using Faraday's first law of electrolysis: \( m = zIt \)
Given:
\( z = 3.3 \times 10^{-7} \; \text{kgC}^{-1} \)
\( I = 4 \; \text{A} \)
\( t = 2 \; \text{hours} = 2 \times 3600 = 7200 \; \text{s} \)\[ m = (3.3 \times 10^{-7}) \times 4 \times 7200 \] \[ m = (3.3 \times 10^{-7}) \times 28800 \] \[ m = 0.009504 \; \text{kg} \] In scientific notation: \( 9.5 \times 10^{-3} \; \text{kg} \).

Neon is well known for its distinct reddish-orange glow when used in gas discharge tubes (neon signs). Other gases produce different colors: Mercury vapor typically produces blue/violet light, and Argon produces a pale lavender or blue glow.

The seven fundamental SI units are the metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity). The Newton (N) is a derived unit used for force, defined as \[ 1 \; \text{N} = 1 \; \text{kg} \cdot \text{m/s}^2 \]

Compare the changes in mass number (A) and atomic number (Z):
Change in A: \( 210 - 206 = 4\)
Change in Z: \( 82 - 80 = 2 \)
An alpha particle (\( ^{4}_{2}He \)) has a mass of 4 and an atomic number of 2. Since the reduction in both numbers perfectly matches the composition of one alpha particle, the decay involves the emission of exactly one alpha particle.

The equation shows two light nuclei (isotopes of Hydrogen, likely Deuterium) combining to form a heavier nucleus (an isotope of Helium) and a neutron, accompanied by the release of energy. The process of combining light nuclei to form a heavier one is called nuclear fusion.