1997E1. A technician uses the circuit shown above to test prototypes of a new battery design. The switch is closed, and the technician records the current for a period of time. The curve that best fits the results is shown in the graph below.
The equation for this curve is I=I0e−kt where t is the time elapsed from the instant the switch is closed and Io and k are constants.
a. i. Using the information in the graph, determine the potential difference Vo across the resistor immediately after the switch is closed.
ii. Would the open circuit voltage of the fresh battery have been less than, greater than, or equal to the value in part i? Justify your answer.
b. Determine the value of k from this best-fit curve. Show your work and be sure to include units in your answer.
c. Determine the following in terms of R,Io,k, and t .
i. The power delivered to the resistor at time t=0
ii. The power delivered to the resistor as a function of time t
iii. The total energy delivered to the resistor from t=0 until the current is reduced to zero