Concept explainers
The charge cycle shown in Figure P2.4 is an example of a three-rate charge. The current is held constant at 30 mA for 6 h. Then it is switched to 20 mA for the next 3 h. Find:
a. The total charge transferred Lo the battery.
b. The energy transferred to the battery.
Hint: Recall that energy w is the integral of power, or
(a)
The total charge transferred to the battery.
Answer to Problem 2.4HP
The total charge delivered to the battery is
Explanation of Solution
Calculation:
The given diagram for the battery voltage graph is shown below.
The given diagram is shown in Figure 1
The given diagram for the battery current is shown in Figure 2
The conversion of
The conversion of
The conversion of
The conversion of
The conversion of
The conversion of
The expression for the current for the entire cycle is given by,
The formula for the charge delivered to the battery is calculated as,
Solve further as,
Conclusion:
Therefore, the total charge delivered to the battery is
(b)
The energy that is transferred to the battery.
Answer to Problem 2.4HP
The total power delivered to the battery is
Explanation of Solution
Calculation:
The line equations for the points that joins the point
The line equations for the points that joins the point
The line equations for the points that joins the point
The evaluated value of the battery voltage for different cycles is shown below,
The formula to calculate power supplied by the battery is given by,
Substitute
Substitute
Substitute
The formula for the relation between the power delivered and the energy stored is given by,
The powered delivered to the battery is calculated as,
Conclusion:
Therefore, the total power delivered to the battery is
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Chapter 2 Solutions
Principles and Applications of Electrical Engineering
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