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A couple of suggestions: (1) the EE stackexchange site a better home for this question (2) simply solve for the voltage across the capacitor and the current through the inductor. Once you have those, the energies stored, as a function of time are just $$W_L(t) = \frac{L}{2}i^2_L$$ and $$W_C(t) = \frac{C}{2}v^2_C$$ Since this is evidently a DC circuit ...

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How do I identify which ones are parallel or series? If all of the current leaving one resistor enters another resistor, the two resistors are in series. The resistances of series connected resistors can be added together to find the equivalent resistance of a single resistor, e.g., $$R_{eq} = R_1 + R_2$$ If all of the voltage across one resistor is ...

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The inherent idea is, from that equation $$I = \exp (\frac{eU}{k_B T})$$ if you plot $(\ln I)$ versus $U$, that would be a straight line (of the form $y=mx$), with a slope $$\alpha = \frac{e}{k_B T}$$ That's all you have to do in the experiment, use least square fitting to find an accurate value of $\alpha$ and then find the Boltzmann constant using the ...

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