Concept explainers
Suppose the current through a wire is given by the curve shown in Figure P2.9.
a. Find the amount of charge q that flows through the wire between
b. Repeatpartafor
c. Sketch
(a)
The amount of current that flows through the wire for the given time.
Answer to Problem 2.9HP
The current that flows though the wire for the time interval
Explanation of Solution
Calculation:
The given time is
The conversion from
The conversion from
The conversion from
The conversion from
The given diagram is shown in Figure 1.
The expression for the current as a function of time is given by,
The slope of the line that represents the current from
The current for the time interval
The expression for the charge that flows through the wire for the time interval
Substitute
Conclusion:
Therefore, the charge that flows though the wire for the time interval
(b)
The charge that flows through the given time interval.
Answer to Problem 2.9HP
The charge that will flow through the wire form
Explanation of Solution
Calculation:
The given time interval is
The slope of the line that represents the current from
The conversion of
The conversion of
The conversion of
The current for the time interval
Substitute
Substitute
The expression for the charge stored from
Substitute
Substitute
Solve further as,
The expression for the charge stored from
Substitute
Substitute
Solve further as,
The mathematical expression for the straight line that represents the current waveform from
The expression for the charge stored from
Substitute
Solve further as,
The mathematical expression for the straight line that represents the current waveform from
The expression for the charge stored from
Substitute
The mathematical expression for the straight line that represents the current waveform from
The expression for the charge stored from
Substitute
The mathematical expression for the straight line that represents the current waveform from
The expression for the charge stored from
Substitute
The current is zero for
The expression for the charge stored from
Substitute
The charge stored from
Substitute
The charge stored from
Substitute
Conclusion:
Therefore, the charge that will flow through the wire form
(c)
To sketch:
The graph for
Answer to Problem 2.9HP
The sketch for
Explanation of Solution
Calculation:
The expression for the current for different time interval is given by,
The integration of the above equation with respect to time to obtain the charge expression is given by,
The evaluated form for the expression of charge for the different time interval is given by,
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The sketch of
The required diagram is shown in Figure 2.
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Chapter 2 Solutions
Principles and Applications of Electrical Engineering
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