Concept explainers
Find the Thévenin equivalent network seen by the capacitor C in Figure P4.76. Use the result and voltage division to determine
The Thevenin equivalent of the network seen by the capacitor
Answer to Problem 4.76HP
The Thevenin equivalent of the network seen by the capacitor
Explanation of Solution
Calculation:
The given diagram is shown in Figure 1
The conversion from
The conversion from
The conversion from
The conversion from
The general form for the expression of voltage is,
The given expression for voltage is given by,
From above and equation (1) the value of angular frequency is given by,
The phasor form of the source voltage is given by,
Substitute
The given expression for current is given by,
The expression for the phasor form of the current is given by
From above and from equation (2) the expression for the phasor form of the current is given by,
The expression to calculate inductive impedance of the inductor is given by,
Substitute
The expression to calculate the capacitive reactance is given by,
Substitute
Mark the values and redraw the circuit for the frequency domain.
The required diagram is shown in Figure 2
To obtain the Thevenin equivalent of the circuit, open circuit the capacitor and redraw the circuit.
The required diagram is shown in Figure 3
From above figure the value of current
Substitute
Apply KVL to the first loop.
Substitute
Apply KVL to the loop on the left.
Substitute
To determine the Thevenin equivalent impedance, short circuit the voltage source and open circuit the current source and redraw the circuit.
The required diagram is shown in Figure 4
From the above figure, the expression for the Thevenin equivalent impedance is given by,
Mark the values and draw the Thevenin equivalent of the circuit.
The required diagram is shown in Figure 5
From the above figure the voltage across the capacitor is calculated as,
The general form for the expression of voltage across the capacitor is given by,
From above and from equation (3), the general form of the voltage across the capacitor is given by,
Substitute
Conclusion:
Therefore, the Thevenin equivalent of the network seen by the capacitor
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Chapter 4 Solutions
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