At ω = 103 rad/s, find the input admittance of each of the circuits in Fig. 9.74.
Figure 9.74
(a)
Find the value of input admittance
Answer to Problem 67P
The value of input admittance
Explanation of Solution
Given data:
Refer to Figure 9.74(a) in the textbook.
The value of angular frequency
Formula used:
Write a general expression to calculate the impedance of a resistor.
Here,
Write a general expression to calculate the impedance of an inductor.
Here,
Write a general expression to calculate the impedance of a capacitor.
Here,
Write a general expression to calculate the input admittance.
Here,
Calculation:
The given circuit is redrawn as shown in Figure 1.
Use equation (1) to find
Use equation (1) to find
Substitute
Substitute
The impedance diagram of Figure 1 is drawn as shown in Figure 2.
Refer to Figure 2, the impedance
The input impedance
Substitute
Conclusion:
Thus, the value of input admittance
(b)
Find the value of input admittance
Answer to Problem 67P
The value of input admittance
Explanation of Solution
Calculation:
The given circuit is also redrawn as shown in Figure 3.
Use equation (1) to find
Use equation (1) to find
Use equation (1) to find
Substitute
Substitute
The impedance diagram of Figure 3 is drawn as shown in Figure 4.
Refer to Figure 4, the impedances
The equivalent impedance
Now, the Figure 4 is reduced as shown in Figure 5.
Refer to Figure 5, the impedance
The input impedance
Substitute
Conclusion:
Thus, the value of input admittance
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