v(t) (V)* 1 0 1 2 t(s) Figure P7.11 7.11. Consider the triangular voltage waveform v(t) shown in Figure P7.11. (a) Express v(t) mathematically. (b) Use the real-shifting property to find L{v(t)}. (c) Sketch the first derivative of v(t).

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Also, express the signum function in terms of the unit step function.

Energy harvesting is the process by which energy is acquired from existing energy sources. In an energy harvesting project a magnetic field is to be generated using an alternating voltage source. An induction coil is to be placed at a suitable distance from the electromagnet in the magnetic field to power a lightbulb. you are required to design the electromagnet and the harvester induction circuits. For the electromagnetic circuit, you have been supplied with with a sinusoidal voltage source, A current limiting resistor of 50 ohms and a copper rod. For the harvester circuit, you have been supplied with a light bulb and an induction coil. For a lit bulb the maximum allowed current is 0.2 A. When the bulb is on its internal resistance can be considered as a resistor of 15 ohms. The induction coil has a cross-sectional area of 1 cm² and 15 turns of wire. Determine the maximum AC voltage amplitude required in the electromagnet circuit to light the bulb if the induction coil is placed 1 cm…