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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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Solved: Repeat charge and discharge currents of 30 A. The

Chapter 25, Problem 82P

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QUESTION:

Problem 82P

Repeat Problem with charge and discharge currents of 30 A. The charging and discharging times will now be 1.7 h rather than 5.0 h. What differences in performance do you see?

Problem:

A 12.0-V battery has an internal resistance of 0.24 Ω and a capacity of 50.0 A-h. The battery is charged by passing a 10-A current through it for 5.0 h. (a) What is the terminal voltage during charging? (b) What total electrical energy is supplied to the battery during charging? (c) What electrical energy is dissipated in the internal resistance during charging? (d) The battery is now completely discharged through a resistor again with a constant current of 10 A. What is the external circuit resistance? (e) What total electrical energy is supplied to the external resistor? (f) What total electrical energy is dissipated in the internal resistance? (g) Why are the answers to parts (b) and (e) not the same?

Exercise:

The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours (A·h). A 50-A·h battery can supply a current of 50 A for 1.0 h, or 25 A for 2.0 h, and so on. (a) What total energy can be supplied by a 12-V, 60-A · h battery if its internal resistance is negligible? (b) What volume (in liters) of gasoline has a total heat of combustion equal to the energy obtained in part (a)? (See Section 17.6; the density of gasoline is 900 kg/m3.) (c) If a generator with an average electrical power output of 0.45 kW is connected to the battery, bow much time will be required for it to charge the battery fully?

Questions & Answers

QUESTION:

Problem 82P

Repeat Problem with charge and discharge currents of 30 A. The charging and discharging times will now be 1.7 h rather than 5.0 h. What differences in performance do you see?

Problem:

A 12.0-V battery has an internal resistance of 0.24 Ω and a capacity of 50.0 A-h. The battery is charged by passing a 10-A current through it for 5.0 h. (a) What is the terminal voltage during charging? (b) What total electrical energy is supplied to the battery during charging? (c) What electrical energy is dissipated in the internal resistance during charging? (d) The battery is now completely discharged through a resistor again with a constant current of 10 A. What is the external circuit resistance? (e) What total electrical energy is supplied to the external resistor? (f) What total electrical energy is dissipated in the internal resistance? (g) Why are the answers to parts (b) and (e) not the same?

Exercise:

The capacity of a storage battery, such as those used in automobile electrical systems, is rated in ampere-hours (A·h). A 50-A·h battery can supply a current of 50 A for 1.0 h, or 25 A for 2.0 h, and so on. (a) What total energy can be supplied by a 12-V, 60-A · h battery if its internal resistance is negligible? (b) What volume (in liters) of gasoline has a total heat of combustion equal to the energy obtained in part (a)? (See Section 17.6; the density of gasoline is 900 kg/m3.) (c) If a generator with an average electrical power output of 0.45 kW is connected to the battery, bow much time will be required for it to charge the battery fully?

ANSWER:

Solution 82P

Step 1

(a) The internal resistance is .

The current through the battery is

Hence the voltage across the resistance is

Now the initial potential difference of the battery is

Hence the terminal voltage is

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