Concept explainers
(a)
The capacitor voltage
Answer to Problem 5.71HP
The value of the capacitor voltage
Explanation of Solution
Calculation:
The given diagram is shown in Figure 1
For time
The required diagram is shown in Figure 2
From above, the expression for the initial voltage across the capacitor is given by,
The expression for the voltage across the capacitor for time
Substitute
Conclusion:
Therefore, the value of the capacitor voltage
(b)
The capacitor voltage
Answer to Problem 5.71HP
The value for the voltage across the capacitor at time
Explanation of Solution
Calculation:
The conversion from
The conversion from
The expression for the current flowing through the inductor for time
The inductor opposes sudden change in the current, thus the current
Substitute
Mark the values and redraw the diagram for time
The required diagram is shown in Figure 3
Apply KVL in the above circuit.
The standard second order equation for the differential equation.
From above and from equation (1), the angular frequency is derived as,
Substitute
The expression for the damping coefficient is given by,
Substitute
The value of
The expression to calculate the damping frequency of the circuit is given by,
Substitute
The expression for the output response of the capacitor is given by,
Substitute
Substitute
Substitute
The differentiation of equation (3) with respect to
Substitute
The expression for the current through the inductor and the capacitor is same and is given by,
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
Therefore, the value for the voltage across the capacitor at time
(c)
The capacitor voltage
Answer to Problem 5.71HP
The final voltage across the capacitor for the time
Explanation of Solution
Calculation:
For time
The required diagram is shown in Figure 4
From the above circuit, the circuit is source free and the final voltage across the capacitor is given by,
Conclusion:
Therefore, the final voltage across the capacitor for the time
(d)
The value of maximum capacitor voltage.
Answer to Problem 5.71HP
The value of maximum capacitor voltage is
Explanation of Solution
Calculation:
The maximum capacitor voltage is obtained by evaluating the expression for voltage across the capacitor equal to zero and is given by,
Substitute
Solve further as,
Substitute
Conclusion:
Therefore, the value of maximum capacitor voltage is
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Chapter 5 Solutions
Principles and Applications of Electrical Engineering
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