$($b$)$ Figure Q$2$ shows the current profile applied to a battery and the

resulting behaviour of the terminal voltage.

i$.$ Estimate the internal resistance of the battery as in the $R_{\text{i}\text{n}\text{t}}$

model.

ii$.$ Copy the measured terminal voltage and on the same axes

sketch the terminal voltage that would be output by the $R_{{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}}$ model

using your estimate of internal resistance, for the same current

profile.

iii. Give an advantage and a disadvantage of this type of model.

iv$.$ Estimate the parameters of the battery as in the Thevenin model.

v$.$ Explain how the Thevenin model could be further developed to

improve accuracy.

$($c$)$ For the battery described in part $($b$),$ at t$=30$ seconds calculate the

cooling power which would be required to achieve thermal equilibrium.