2. a) Design a 9v DC oscillator circuit that produces a frequency of 500 Hz. The circuit may use a 555 timer or two transistor design(s). Show all calculations including the DC currents and bias voltages. Include the schematic and the required frequency formula(s).   b) As a bonus, if a larger load were required to be connected to the chip, how would the schematic look and what components would be used to do design it? Also, as a theoretical approximation, if the 9v battery had a rating of 4 amp-hours, how long would it last powering this circuit? Show calculations to illustrate how you arrived at the answer.

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Maximum power transfer theorem

A resistive load will consume maximum power from a network when the load resistance is equal to the resistance of the network as viewed from the open-circuit terminals, with all energy sources removed leaving only the internal resistances. Physicist Moritz von Jacobi introduced the maximum power transfer theorem in 1940. Therefore, this theorem is also known as Jacobi's law.