CHAPTER 2  >  ACTIVITIES  >  PROBLEMS  >  PROBLEM 4
Battery characteristic and maximum power
A battery is investigated. One by one, resistors having different resistances are attached to a simple circuit and voltages and the electric current are measured as shown in the figure.

a. Determine the open circuit voltage, the short circuit current, and the internal resistance of the battery.
b. Use a resistor having a resistance of 1.5 ohm with the battery. How long will it take until energy equal to 100 J has be released in the resistor? How much energy has been dissipated in the battery during the same period? How much energy has been released by the chemical reactions in the battery during the same period?
c. Calculate the electric power of the battery for the data in the graph. Draw a diagram showing the power as a function of U_S. Determine the maximum power and the value of U_S for maximum power.
d. Derive the condition for maximum power from the model of the battery having an internal resistor with constant resistance.
e. A capacitor having a constant capacitance of 1.0 F is place in a simple circuit with the battery and a 2.0 ohm external resistor. Construct as carefully as possible the voltage across the capacitor as a function of time during charging. What is the time constant of the circuit?
f. For the process of charging of the capacitor, explain the relation between (1) the energy released as a consequence of chemical reactions, (2) the energy dissipated in the resistor and the battery, and (3) the energy stored in the capacitor.





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