The time
Answer to Problem 5.79HP
The value of
Explanation of Solution
Calculation:
The given circuit is shown in Figure 1
For time
The required diagram is shown in Figure 2
The value for the current through the resistance of
The value for the current through the resistance of
The expression for the initial voltage across the capacitor
Substitute
The expression for the initial voltage across the capacitor
Substitute
For time
The required diagram is shown in Figure 3
Apply KCL to the node
Substitute
Apply KCL to the node
Substitute
Substitute
The standard second order equation for the above equation is given by,
From above and from equation (2), the natural frequency of the circuit is calculated as,
The damping ratio of the circuit is calculated as,
Substitute
The general equation for the voltage across the capacitor is given by,
Substitute
Substitute
Substitute
Substitute
Apply KCL to the node
Substitute
Substitute
The differentiation of equation (3) with respect to
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the value of
Conclusion:
Therefore, the value of
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Chapter 5 Solutions
Principles and Applications of Electrical Engineering
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