Answer :
Final answer:
Without the knowledge of how the capacitors are interconnected or the applied voltage, we can only confirm that the capacitors must be in series. However, none of the provided options for C3 produces a feasible value for voltage.
Explanation:
The question involves finding the value of capacitance C3 in a series of capacitors given certain conditions. Since the capacitors are assumed to be in series, the total capacitance must be lower than the smallest capacitor. That means the equivalent capacitance of the complete network is less than 4.00 µF. Also, the potential energy stored in a capacitor is given by U=1/2*CV², So, if total energy is 2.70×10−3 J, and equivalent capacitance (C) of the complete network is assumed to be less than 4.00 µF, then the square root of (2*U/C) should give us a value that is feasible for voltage (V). Now, none of the given options for C3 can provide a value for voltage (V) within a typical range and thus validates the assumption that the capacitance must be in series. However, for a more exact value of C3, we would need to know more information about how these capacitors are interconnected and also about the voltage applied to them.
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