An exploratory deep-space scientific probe uses a small nuclear fission reactor to continuously generate an electrical power of 250 kW250\text{ kW}250 kW. To achieve high propulsion, the probe is equipped with a pulsed electromagnetic plasma thruster that requires a massive, rapid release of energy.
To power each pulse, energy from the reactor is accumulated over time in a heavy-duty capacitor bank. When this capacitor bank is fully charged:
Calculate the total capacitance, CCC, of the capacitor bank.
Explain why the individual capacitors in the bank must be connected in parallel in order to produce this total capacitance.
The total stored energy must be fully discharged into the thruster's electromagnetic coils in a time of less than 0.15 ms0.15\text{ ms}0.15 ms.
Explain, using a calculation, why the thruster is powered by the capacitor bank instead of being connected directly to the probe's 250 kW250\text{ kW}250 kW nuclear reactor.
The onboard nuclear reactor relies on the following fission reaction:
n+235U→141Ba+92Kr+3n \text{n} + {}^{235}\text{U} \rightarrow {}^{141}\text{Ba} + {}^{92}\text{Kr} + 3\text{n} n+235U→141Ba+92Kr+3nCalculate the number of individual fission reactions that must occur to release a total amount of nuclear energy equal to the electrical energy stored in the capacitor bank.
