1. An AC dimmer shown in Figure 1 is used to adjust brightness of incandescent bulb by varying the value of resistor Rs. Derive an equation for the power consumed in bulb as a function of adjustable resistance Rs. Plot variation of lamp power in percent of full power as a function of Rs from 4 k? to 570 k? (minimum step size is 500 ?). Supply voltage is 220 V, 50 Hz AC sinusoidal voltage. Lamp rated power is 500 W, Cs = 0.1 µF and break over voltage of diac is ±32 V. Please note that derivation is required - direct copying of formulas from some other sources are not allowed. Show all calculations to get full credit and include any computer program listings that you use.
Q2. Two 1.2V, 2100mAh NiMh (Nickel Metal Hydride) batteries (model number: Panasonic BK210A) are connected in series to supply a DC voltage of 5V and a DC current of 1A to a portable charger for your cellular phone. In order to achieve small footprint (small size and low weight), the switching frequency must be 100 kHz. The inductor current ripple and output voltage ripple is 10% and 1% of their averaged values, respectively. Draw the complete circuit schematic that will achieve this conversion and determine the values of all circuit elements. What are the average values of input current, input power, and output power? Determine the total operational time in minutes and total energy in Joules delivered to load for a fully charged battery considering the discharge curve of batteries given in the manufacturer datasheets and using end of termination voltage of 1.0V. Assume ideal semiconductor devices and steady-state operation.