This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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V_3 = 1.2\,A × 2\, V_3 = 2.4\,V The voltmeter reading will be 2.4 V. 8. (a) i) • Increase the speed of the magnet: Moving the magnet faster into or out of the solenoid increases the rate of change of magnetic flux linkage, which induces a larger electromotive force (e.m.f.) and thus a larger current. • Increase the number of turns in the solenoid: A solenoid with more turns will have more conductors cutting the magnetic field lines for the same movement, leading to a larger induced e.m.f. and current. ii) Step 1: Apply Lenz's Law. As the North pole of the magnet moves into the solenoid, an induced current will flow to create a magnetic field that opposes this motion. To oppose the incoming North pole, end X of the solenoid must become a North pole. The polarity of end X of the solenoid is North pole. 8. (b) i) Points A and D are in phase. Explanation: Both points A and D represent crests of the wave, meaning they have the same maximum positive displacement and are at the same stage of their oscillation. ii) The distance from A to D represents one wavelength. Explanation: This distance covers one complete cycle of the wave, from one crest to the next consecutive crest. iii) Step 1: Identify given values. Wavelength, = 0.8\,m Speed, v = 20\,m/s Step 2: Use the wave speed formula to calculate frequency. The relationship between speed, frequency, and wavelength is v = f . Rearrange to solve for frequency: f = (v)/(). f = 20\,m/s0.8\,m f = 25\,Hz The frequency of the wave is 25 Hz. iv) • Wave pulse: A single, non-repeating disturbance or short burst of energy that travels through a medium. • Wave train: A continuous series of periodic waves that propagates through a medium, consisting of multiple wave cycles. 8. (c) • Promoting the use of renewable energy sources: Shifting from fossil fuels to sources like solar, wind, and hydroelectric power reduces air pollution and greenhouse gas emissions. • Implementing stricter regulations on industrial emissions and waste disposal: This ensures that factories and industries release fewer pollutants into the air and water, and manage their waste responsibly.