Change in Capacitor for largest possible Current

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To achieve the largest possible current from the source, the capacitive reactance must be calculated based on the given frequency and inductance. The inductive reactance is determined to be 17.2 Ω, while the capacitive reactance for a 2.55 mF capacitor at 49.1 Hz is calculated as 1.27 Ω. The total impedance of the RLC circuit, which includes a resistor of 21.1 Ω, is found to be 26.4 Ω. Clarification is sought regarding the nature of the circuit configuration and the signs of reactance. Understanding the series RLC circuit configuration is essential for accurate calculations.
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Homework Statement


The capacitor is changed so that the largest possible current is supplied by the source.
Enter the value of the capacitive reactance when this change is made.
Give your answer in Ohms (Ω). A unit is not required with your answer.

Homework Equations


The circuit is powered by an alternating voltage source, which produces a voltage that varies sinusoidally and has an RMS voltage of V.

- The frequency of the voltage source is 49.1 Hz and the inductor has an inductance of 55.9 mH.
Calculate the inductive reactance (XL) of the inductor.
Give your answer in units of Ohms (Ω) = 17.2

- The capacitor has a capacitance of 2.55 mF.
Calculate the capacitive reactance (XC) of the capacitor. The frequency is still 49.1 Hz.
Again, give your answer in units of Ohms (Ω) = 1.27

- The resistor has a resistance of 21.1 Ω.
Calculate the impedance (Z) of the RLC network.
Give your answer in units of Ohms (Ω) = 26.4

Im not sure what this question is asking me or what equation to use to calculate it either.
 
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What is the sign of the capacitive reactance and inductive reactance?
 
How are your components interconnected? Is it a series RLC circuit like this?

upload_2018-5-26_12-13-11.png
 

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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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